The aim of this thesis is to show that the use of heavy-tailed distributions in finance is theoretically unfounded and may cause significant misunderstandings and fallacies in model interpretation. The main reason seems to be a wrong understanding of the concept of the distributional tail. Also in models based on real data it seems more reasonable to concentrate on the central part of the distribution not tails. Powered by TCPDF (www.tcpdf.org)

Cette thèse présente plusieurs aspects de la croissance stochastique des interfaces, par lebiais de son modèle le plus étudié, l'équation de Kardar-Parisi-Zhang (KPZ). Bien qued'expression très simple, cette équation recèle une grande richesse phénoménologiqueet est l'objet d'une recherche intensive depuis des dizaines d'années. Cela a conduit àl'émergence d'une nouvelle classe d'universalité, contenant des modèles de croissanceparmi les plus courants, tels que le Eden model ou encore le Polynuclear Growth Model.L'équation KPZ est également reliée à des problèmes d'optimisation en présence dedésordre (le Polymère Dirigé), ou encore à la turbulence des uides (l'équation de Burger), renforçant son intérêt. Cependant, les limites de cette classe d'universalitésont encore mal comprises. L'objet de cette thèse est, après avoir présenté les progrèsles plus récents dans le domaine, de tester les limites de cette classe d'universalité. Lathèse s'articule en quatre parties :i) Dans un premier temps, nous présentons des outils théoriques qui permettent decaractériser finement l'évolution de l'interface. Ces outils montrent une grande flexibilité, que nous illustrons en considérant le cas d'une géométrie confinée (une interfacecroissant le long d'une paroi).ii) Nous nous penchons ensuite sur l'influence du désordre, et plus particulièrementl'importance des évènements extrêmes dans la mécanique de croissance. Les largesfluctuations du désordre déforment l'interface et conduisent à une modification notabledes exposants de scaling. Nous portons une attention particulière aux conséquencesd'un tel désordre sur les stratégies d'optimisation en milieu désordonné.iii) La présence de corrélations dans le désordre est d'un intérêt expérimentalimmédiat. Bien qu'elles ne modifient pas la classe d'universalité, elles influent grandement sur la vitesse de croissance moyenne de l'interface. Cette partie est dédiée àl'étude de cette vitesse moyenne, souvent négligée car délicate à définir, et à l'existenced'un optimum de croissance intimement lié à la compétition entre exploration et exploitation.iv) Enfin, nous considérons un exemple expérimental de croissance stochastique (quin'appartient toutefois pas à la classe KPZ) et développons un formalisme phénoménologiquepour modéliser la propagation d'une interface chimique dans un milieu poreux désordonné.Tout au long du manuscrit, les conséquences des phénomènes observées dans desdomaines variés, tels que les stratégies d'optimisation, la dynamique des populations,la turbulence ou la finance, sont détaillées. / This Thesis presents several aspects of the stochastic growth, through its most paradig-matic model, the Kardar-Parisi-Zhang equation (KPZ). Albeit very simple, this equa-tion shows a rich behaviour and has been extensively studied for decades. The existenceof a new universality class is now well established, containing numerous growth modelslike the Eden model or the Polynuclear Growth Model. The KPZ equation is closelyrelated to optimisation problems (the Directed Polymer) or turbulence of uids (theBurgers equation), a feature that underlines its importance. Nonetheless, the bound-aries of this universality class are still vague. The focus of this Thesis is to probe thoselimits through various modifications of the models. It is divided in four chapters:i) First, we present theoretical tools, borrowed from integrable systems, that allowto characterize in great details the evolution of the interface. Those tools exhibitconsiderable exibility due to the large corpus of work on integrable systems, and weillustrate it by tackling the case of confined geometry (growth close to a hard wall).ii) We investigate the inuence of the disorder distribution, and more specificallythe importance of large events, with heavy-tailed distributions. Those extreme eventsstretch the interface and notably modify the main scaling exponents. The consequenceson optimization strategies in disorder landscapes are emphasized.iii) The presence of correlations in the disorder is of natural experimental interest.Although they do not impact the KPZ class, they greatly inuence the average speed ofgrowth. The latter quantity is often overlooked because it is non-universal and ratherill-defined. Nonetheless, we show that a generic optimal average speed exists in presenceof time correlations, due to a competition between exploration and exploitation.iv) Finally, we consider a set of experiments about chemical front growth in porousmedium. While this growth process is not related to KPZ in an immediate way, wepresent different tools that effciently reproduce the observations.Along that work, the consequences of each Chapter in various domains, like opti-misation strategies, turbulence, population dynamics or finance, are detailed.

Les modèles linéaires généralisés (GLMs) constituent l’une des classes de modèles les plus populaires en statistique. Cette classe contient une grande variété de modèles de régression fréquemment utilisés, tels que la régression linéaire normale, la régression logistique et les gamma GLMs. Dans les GLMs, la distribution de la variable de réponse définit une famille exponentielle. Un désavantage de ces modèles est qu’ils ne sont pas robustes par rapport aux valeurs aberrantes. Pour les modèles comme la régression linéaire normale et les gamma GLMs, la non-robustesse est une conséquence des ailes exponentielles des densités. La différence entre les tendances de l’ensemble des données et celles des valeurs aberrantes donne lieu à des inférences et des prédictions biaisées. A notre connaissance, il n’existe pas d’approche bayésienne robuste spécifique pour les GLMs. La méthode la plus populaire est fréquentiste ; c’est celle de Cantoni and Ronchetti (2001). Leur approche consiste à adapter les M-estimateurs robustes pour la régression linéaire au contexte des GLMs. Cependant, leur estimateur est dérivé d’une modification de la dérivée de la log-vraisemblance, au lieu d’une modification de la vraisemblance (comme avec les M-estimateurs robustes pour la régression linéaire). Par conséquent, il n’est pas possible d’établir une correspondance claire entre la fonction modifiée à optimiser et un modèle. Le fait de proposer un modèle robuste présente deux avantages. Premièrement, il permet de comprendre et d’interpréter la modélisation. Deuxièmement, il permet l’analyse fréquentiste et bayésienne. La méthode que nous proposons s’inspire des idées de la régression linéaire robuste bayésienne. Nous adaptons l’approche proposée par Gagnon et al. (2020), qui consiste à utiliser une distribution normale modifiée avec des ailes plus relevées pour le terme d’erreur. Dans notre contexte, la distribution de la variable de réponse est une version modifiée où la partie centrale de la densité est conservée telle quelle, tandis que les extrémités sont remplacées par des ailes log-Pareto, se comportant comme (1/|x|)(1/ log |x|)λ. Ce mémoire se concentre sur les gamma GLMs. La performance est mesurée à la fois théoriquement et empiriquement, avec une analyse des données sur les coûts hospitaliers. / Generalized linear models (GLMs) form one of the most popular classes of models in statistics. This class contains a large variety of commonly used regression models, such as normal linear regression, logistic regression and gamma GLMs. In GLMs, the response variable distribution defines an exponential family. A drawback of these models is that they are non-robust against outliers. For models like the normal linear regression and gamma GLMs, the non-robustness is a consequence of the exponential tails of the densities. The difference in trends in the bulk of the data and the outliers yields skewed inference and prediction. To our knowledge, there is no Bayesian robust approach specifically for GLMs. The most popular method is frequentist; it is that of Cantoni and Ronchetti (2001). Their approach is to adapt the robust M-estimators for linear regression to the context of GLMs. However, their estimator is derived from a modification of the derivative of the log-likelihood, instead of from a modification of the likelihood (as with robust M-estimators for linear regression). As a consequence, it is not possible to establish a clear correspondence between the modified function to optimize and a model. Having a robust model has two advantages. First, it allows for an understanding and an interpretation of the modelling. Second, it allows for both frequentist and Bayesian analysis. The method we propose is based on ideas from Bayesian robust linear regression. We adapt the approach proposed by Gagnon et al. (2020), which consists of using a modified normal distribution with heavier tails for the error term. In our context, the distribution of the response variable is a modified version where the central part of the density is kept as is, while the extremities are replaced by log-Pareto tails, behaving like (1/|x|)(1/ log |x|)λ. The focus of this thesis is on gamma GLMs. The performance is measured both theoretically and empirically, with an analysis of hospital costs data.

Nous présentons d’abord une introduction au sujet des marches aléatoires en milieux aléatoires. Nous nous penchons en particulier sur les phénomènes de ralentissement, et plus précisément sur la propriété de vieillissement qu’exhibent plusieurs de ces systèmes lorsque les paramètres sont tels qu’ils conduisent l’environnement aléatoire à produire fréquemment des « pièges », soient des structures qui retiennent la marche aléatoire dans la même région de l’environnement pour de longues durées de temps. Nous illustrons ces notions à l’aide de résultats connus pour deux modèles. Nous présentons par la suite une preuve pour une propriété de vieillissement dans le cas de la marche aléatoire biaisée sur les conductances aléatoires à queues lourdes dans la grille infinie hyper-cubique à d dimensions, qui est le sujet d’un article en attente de publication. / We first present an introduction to the topic of random walks on random environments (RWRE). In particular, we look at slow-down phenomena and, more specifically, ageing properties exhibited by multiple such systems when parameters are chosen such that the random environment frequently produces large “traps”: structures that hold up the progress of the random walk by keeping it in the same region of the environment for long periods of time. We illustrate these behaviours by presenting known results for two such models. We then present a proof for an ageing property in the case of the biased random walk on heavy-tailed random conductances in the infinite hyper-cubic lattice in d dimensions; this is the subject of a research article pending publication.

This thesis concentrates on different approaches of solving decision making problems with an aspect of randomness. The basic methodologies of converting stochastic optimization problems to deterministic optimization problems are described. The proximity of solution of a problem and its empirical counterpart is shown. The empirical counterpart is used when we don't know the distribution of the random elements of the former problem. The distribution with heavy tails, stable distribution and their relationship is described. The stochastic dominance and the possibility of defining problems with stochastic dominance is introduced. The proximity of solution of problem with second order stochastic dominance and the solution of its empirical counterpart is proven. A portfolio management problem with second order stochastic dominance is solved by solving the equivalent empirical problem. Powered by TCPDF (www.tcpdf.org)

Les principaux objectifs des opérateurs ferroviaires visent à accroître la sécurité, réduire les coûts d’exploitation et de maintenance et augmenter l’attractivité et les bénéfices du transport ferroviaire en offrant de nouveaux services aux passagers. Ceci ne pourra être atteint que grâce à la multiplication des échanges de données entre les différents acteurs du monde ferroviaire. L’interopérabilité, l’efficacité spectrale, l’optimisation de l’usage des ressources radio et l’amélioration de la fiabilité des communications sont des exigences fortes pour les applications de télécommunication ferroviaires. Les recherches dans le domaine de la radio cognitive ont vu le jour afin de répondre aux besoins de communication de l’armée ainsi qu’aux besoins dans les secteurs de la sécurité publique. Ces domaines partagent souvent les mêmes exigences que les chemins de fers. Ainsi, la radio cognitive a montré un potentiel prometteur pour répondre aux besoins listés précédemment. Une des principales fonctionnalités d’un dispositif de radio cognitive est de prendre conscience de son environnement radioélectrique et de détecter les bandes disponibles. Trois principaux éléments définissent l’environnement de la radio cognitive : l’utilisateur, les règles d’accès au spectre radio et les domaines radio. Cette thèse met en avant plusieurs contributions relatives à la reconnaissance de l’environnement radiofréquence et la détection de bandes libres. Plus spécifiquement, ces contributions portent sur la reconnaissance par la radio cognitive de l’occupation du spectre et de la modulation des signaux présents dans les bandes analysées. Ces fonctions ont été conçues pour le contexte ferroviaire, c’est-à-dire la grande vitesse et un environnement électromagnétique difficile en présence de bruit impulsif. / An essential goal of railway operators is to increase safety, reduce operation and maintenance costs, and increase attraction and profit by offering new services to passengers. These objectives will be reached thanks to a huge increase of data fluxes exchanges between railways stakeholders and infrastructures.Interoperability, spectral efficiency, optimization of radio resource usages, and improvement of communications reliability are of significant interest for railway applications. The Cognitive Radio (CR) research has been successfully applied to meet the communication needs of the military as well as the public-safety sectors, which share many of the same needs as railway. CRs have shown significant promise to answer all of the previously listed requirements. One of the main capabilities of a CR device is to sense and finally become aware of its environment. Three major domains define the environment of the CR, namely, the user, policy, and radio domains. This thesis highlights several contributions to radio environment awareness of a CR device. More specifically, these contributions lie in the spectrum awareness and waveform awareness functions of the CR. We designed these functions for the railways context, that is, a high speed vehicular context, besides difficult electromagnetic environments resulting a heavy-tailed impulsive noise.

The continuous progression of urbanization has resulted in an increasing number of people living in cities or towns. In parallel, advancements in technologies, such as the Internet, telecommunications, and transportation, have allowed for better connectivity among people. This has engendered drastic changes in urban systems during the recent decades. From a social geographic perspective, the changes in urban systems are primarily characterized by intensive contacts among people and their interactions with the surrounding urban environment, which further leads to subsequent challenging problems such as traffic jams, environmental pollution, urban sprawl, etc. These problems have been reported to be heterogeneous and non-deterministic. Hence, to cope with them, massive amounts of geographic data are required to create new knowledge on urban systems. Due to the thriving of Volunteer Geographic Information (VGI) in recent years, this thesis presents knowledge on urban systems based on extensive VGI datasets from three sources: highway dataset from the OpenStreetMap (OSM) project, photo location dataset from the Flickr website, and GPS tracking datasets from volunteers, taxicabs, and air flights. The knowledge primarily relates to two issues of urban systems: the urban space and the corresponding human dynamics. In accordance, on one hand, urban space acts as a carrier for associated geographic activities and knowledge of it benefits our understanding of current social and economic problems in urban systems. On the other hand, human dynamics reflect human behavior in urban space, which leads to complex mobility or activity patterns. Its investigation allows a derivation of the underlying driving force that is very instructive to urban planning, traffic management, and infectious disease control. Therefore, to fully understand the two issues, this thesis conducts a thorough investigation from multiple aspects. The first issue is investigated from four aspects. First, at the city level, the controversial topic of city size regularity is investigated in terms of natural cities, and the conclusion is that Zipf’s law holds stably for all US cities. Second, at the sub-city level, the size distribution of spatial units within different cities in terms of the clusters formed by street nodes, photo locations, and taxi static points are explored, and the result shows a remarkable scaling property of these spatial units. Third, enlightened by the scaling property of the urban space at the city or sub-city level, this thesis devises a novel tool that can demarcate the cities into three categories: compact cities, normal cities, and sprawling cities. The tool is then applied to cities in both the US and three European countries. In the last, another representation of urban space is taken into account, namely the transportation network. The findings report that the US airport network displays the properties of scale-free, small-world, and disassortative mixing and that the individual natural airports show heterogeneous patterns that are probably subject to geographic constraints and socioeconomic factors. The second issue is examined from four perspectives. First, at the city level, the movement flow contributed by agents using two types of behavior is investigated through an agent-based simulation, and the result conjectures that the human mobility behavior is mainly shaped by the underlying street network. Second, at the country level, this thesis reports that the human travel length by air can be approximated well by an exponential distribution, and subsequent simulations indicate that human mobility behavior is largely constrained by the underlying airport network. Third, at the regional level, the length that humans travel by car is demonstrated to agree well with a power law with exponential cutoff distribution, and subsequent simulation further reproduces this levy flight characteristic. Based on the simulation, human mobility behavior is again revealed to be primarily shaped by the underlying hierarchical spatial structure. Finally, taxicab static points are adopted to explore human activity patterns, which can be characterized as the regularities in space and time, the heterogeneity and predictability in space. From a complex system perspective, this thesis presents the knowledge discovered in urban systems using massive volumes of geographic data. Together with new knowledge from empirical findings, the development of methods, and the design of theoretic models, this thesis also shares the research community with geographic data generated from extensive VGI datasets and the corresponding source codes. Moreover, this study is aligned with a paradigm shift in that it analyzes large-size datasets using high processing power as opposed to analyzing small-size datasets with low processing power. / <p>QC 20121113</p>

Cette thèse s'inscrit dans le contexte de la statistique des valeurs extrêmes. Elle y apporte deux contributions principales. Dans la littérature récente en statistique des valeurs extrêmes, un modèle de queues de distributions a été introduit afin d'englober aussi bien les lois de type Pareto que les lois à queue de type Weibull. Les deux principaux types de décroissance de la fonction de survie sont ainsi modélisés. Un estimateur des quantiles extrêmes a été déduit de ce modèle mais il dépend de deux paramètres inconnus, le rendant inutile dans des situations pratiques. La première contribution de cette thèse est de proposer des estimateurs de ces paramètres. Insérer nos estimateurs dans l'estimateur des quantiles extrêmes précédent permet alors d'estimer des quantiles extrêmes pour des lois de type Pareto aussi bien que pour des lois à queue de type Weibull d'une façon unifiée. Les lois asymptotiques de nos trois nouveaux estimateurs sont établies et leur efficacité est illustrée sur des données simulées et sur un jeu de données réelles de débits de la rivière Nidd se situant dans le Yorkshire en Angleterre. La seconde contribution de cette thèse consiste à introduire et estimer une nouvelle mesure de risque appelé Conditional Tail Moment. Elle est définie comme le moment d'ordre a>0 de la loi des pertes au-delà du quantile d'ordre p appartenant à ]0,1[ de la fonction de survie. Estimer le Conditional Tail Moment permet d'estimer toutes les mesures de risque basées sur les moments conditionnels telles que la Value-at-Risk, la Conditional Tail Expectation, la Conditional Value-at-Risk, la Conditional Tail Variance ou la Conditional Tail Skewness. Ici, on s'intéresse à l'estimation de ces mesures de risque dans le cas de pertes extrêmes c'est-à-dire lorsque p tend vers 0 lorsque la taille de l'échantillon augmente. On suppose également que la loi des pertes est à queue lourde et qu'elle dépend d'une covariable. Les estimateurs proposés combinent des méthodes d'estimation non-paramétrique à noyau avec des méthodes issues de la statistique des valeurs extrêmes. Le comportement asymptotique de nos estimateurs est établi et illustré aussi bien sur des données simulées que sur des données réelles de pluviométrie provenant de la région Cévennes-Vivarais. / This thesis can be viewed within the context of extreme value statistics. It provides two main contributions to this subject area. In the recent literature on extreme value statistics, a model on tail distributions which encompasses Pareto-type distributions as well as Weibull tail-distributions has been introduced. The two main types of decreasing of the survival function are thus modeled. An estimator of extreme quantiles has been deduced from this model, but it depends on two unknown parameters, making it useless in practical situations. The first contribution of this thesis is to propose estimators of these parameters. Plugging our estimators in the previous extreme quantiles estimator allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unified way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a simulation study and on a real data set of exceedances of the Nidd river in the Yorkshire (England). The second contribution of this thesis is the introduction and the estimation of a new risk measure, the so-called Conditional Tail Moment. It is defined as the moment of order a>0 of the loss distribution above the quantile of order p in (0,1) of the survival function. Estimating the Conditional Tail Moment permits to estimate all risk measures based on conditional moments such as the Value-at-Risk, the Conditional Tail Expectation, the Conditional Value-at-Risk, the Conditional Tail Variance or the Conditional Tail Skewness. Here, we focus on the estimation of these risk measures in case of extreme losses i.e. when p converges to 0 when the size of the sample increases. It is moreover assumed that the loss distribution is heavy-tailed and depends on a covariate. The estimation method thus combines nonparametric kernel methods with extreme-value statistics. The asymptotic distribution of the estimators is established and their finite sample behavior is illustrated both on simulated data and on a real data set of daily rainfalls in the Cévennes-Vivarais region (France).

The study of how social organizations work, change and develop is central to sociology and to our understanding of the social world and its transformations. At the same time, the underlying principles of organizational dynamics are extremely difficult to investigate. This is partly due to the difficulties of tracking organizations, individuals and their interactions over relatively long periods of time. But it is also due to limitations in the kinds of quantitative methods used to tackle these questions, which are for the most part based on regression analysis. This thesis seeks to improve our understanding of social organizing by using models to explore and describe the logics of the structures and mechanisms underlying organizational change. Particular emphasis is given to the modeling process, the use of new concepts and analogies, and the application of interdisciplinary methods to get new insights into classical sociological questions. The thesis consists of an introductory part and five studies (I-V). Using Swedish longitudinal data on employment in the Stockholm Region, the studies tackle different dimensions of organizational dynamics, from organizational structures and growth processes to labor mobility and employment trajectories. The introductory chapters contextualize the studies by providing an overview of theories, concepts and quantitative methods that are relevant for the modeling of organizational dynamics.  The five studies look into various aspects of organizational dynamics with the help of complementary data representations and non-traditional quantitative methods. Study I analyzes organizational growth statistics for different sectors and industries. The typically observed heavy-tailed statistical patterns for the size and growth rate distributions are broken down into a superposition of interorganizational movements. Study II models interorganizational movements as a labor flow network. Organizations tend to be more tightly linked if they belong to the same ownership sector. Additionally, public organizations have a more stable connection structure. Study III uses a similarity-based method called homogeneity analysis to map out the social space of large organizations in the Stockholm Region. A social distance is then derived within this space, and we find that the interorganizational movements analyzed in Studies I and II take place more often between organizations that are closer in social space and in the same network community. Study IV presents an approach to organizational dynamics based on sequences of employment states. Evidence for a positive feedback mechanism is found for large and highly sequence-diverse public organizations. Finally, Study V features an agent-based model where we simulate a social influence mechanism for organizational membership dynamics. We introduce a parameter analogous to a physical temperature to model contextual influence, and the familiar growth distributions are recovered as an intermediate case between extreme parameter values. The thesis as a whole provides suggestions for a more process-oriented modeling approach to social organizing that gives a more prominent role to the logics of organizational change. Finally, the series of methodological tools discussed can be useful for the analysis of many other social processes and more broadly for the development of quantitative sociological methods. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.</p><p> </p>

Numerous studies on Queueing systems, such as Internet traffic flows, have shown to be bursty, self-similar and/or long-range dependent, because of the heavy (long) tails for the various distributions of interest, including intermittent intervals and queue lengths. Other studies have addressed vacation in no-customers’ queueing system or when the server fails. These patterns are important for capacity planning, performance prediction, and optimization of networks and have a negative impact on their effective functioning. Heavy-tailed distributions have been commonly used by telecommunication engineers to create workloads for simulation studies, which, regrettably, may show peculiar queueing characteristics. To cost-effectively examine the impacts of different network patterns on heavy- tailed queues, new and reliable analytical approaches need to be developed. It is decided to establish a brand-new analytical framework based on optimizing entropy functionals, such as those of Shannon, Rényi, Tsallis, and others that have been suggested within statistical physics and information theory, subject to suitable linear and non-linear system constraints. In both discrete and continuous time domains, new heavy tail analytic performance distributions will be developed, with a focus on those exhibiting the power law behaviour seen in many Internet scenarios. The exposition of two major revolutionary approaches, namely the unification of information geometry and classical queueing systems and unifying information length theory with transient queueing systems. After conclusions, open problems arising from this thesis and limitations are introduced as future work.