This dissertation presents a theoretical study of arbitrary discretizations of general nonequilibrium and non-steady-state systems. It will be shown that, without requiring the partitions of the phase-space to fulfill certain assumptions, such as culminating in Markovian partitions, a Markov chain can be constructed which has the same macro-change of probability of the occupation of the states as the original process. This is true for any classical and semiclassical system under any discrete or continuous, deterministic or stochastic, Markovian or non-Markovian dynamics. Restricted to classical and semi-classical systems, a formalism is developed which treats the projection of arbitrary (multidimensional) complex systems onto a discrete set of states of an abstract state-space using time and ensemble sampled transitions between the states of the trajectories of the original process. This formalism is then used to develop expressions for the mean first passage time and (in the case of projections resulting in pseudo-one-dimensional motion) for the individual residence times of the states using just the time and ensemble sampled transition rates. The theoretical work is illustrated by several numerical examples of non-linear diffusion processes. Those include the escape over a Kramers potential and a rough energy barrier, the escape from an entropic barrier, the folding process of a toy model of a linear polymer chain and the escape over a fluctuating barrier. The latter is an example of a non- Markovian dynamics of the original process. The results for the mean first passage time and the residence times (using both physically meaningful and non-meaningful partitions of the phase-space) confirms the theory. With an accuracy restricted only by the resolution of the measurement and/or the finite sampling size, the values of the mean first passage time of the projected process agree with those of a direct measurement on the original dynamics and with any available semi-analytical solution.

L'objectif de cette thèse est de développer la théorie du contrôle stochastique et ses applications en dynamique des populations. D'un point de vue théorique, nous présentons l'étude de problèmes de contrôle stochastique à horizon fini sur des processus de diffusion, de branchement non linéaire et de branchement-diffusion. Dans chacun des cas, nous raisonnons par la méthode de la programmation dynamique en veillant à démontrer soigneusement un argument de conditionnement analogue à la propriété de Markov forte pour les processus contrôlés. Le principe de la programmation dynamique nous permet alors de prouver que la fonction valeur est solution (régulière ou de viscosité) de l'équation de Hamilton-Jacobi-Bellman correspondante. Dans le cas régulier, nous identifions également un contrôle optimal markovien par un théorème de vérification. Du point de vue des applications, nous nous intéressons à la modélisation mathématique du cancer et de ses stratégies thérapeutiques. Plus précisément, nous construisons un modèle hybride de croissance de tumeur qui rend compte du rôle fondamental de l'acidité dans l'évolution de la maladie. Les cibles de la thérapie apparaissent explicitement comme paramètres du modèle afin de pouvoir l'utiliser comme support d'évaluation de stratégies thérapeutiques. / The main objective of this thesis is to develop stochastic control theory and applications to population dynamics. From a theoritical point of view, we study finite horizon stochastic control problems on diffusion processes, nonlinear branching processes and branching diffusion processes. In each case we establish a dynamic programmic principle by carefully proving a conditioning argument similar to the strong Markov property for controlled processes. Then we deduce that the value function is a (viscosity or regular) solution of the associated Hamilton-Jacobi-Bellman equation. In the regular case, we further identify an optimal control in the class of markovian strategies thanks to a verification theorem. From a pratical point of view, we are interested in mathematical modelling of cancer growth and treatment. More precisely, we build a hybrid model of tumor growth taking into account the essential role of acidity. Therapeutic targets appear explicitly as model parameters in order to be able to evaluate treatment strategies.

As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.

Amorphous Silicon(a-Si) films have attracted the attention of several investigators as it is an economical material for devices. One of the problems that is addressed is the doping of these films after they are prepared. In this thesis, we investigated the effects of doping amorphous Sil­icon films(prepared by r.f. sputtering) with Aluminium(Al) by ther­mal diffusion. Amorphous Silicon films have been prepared on glass substrates at optimal process parameters. Then, the a-Si films are coated with Al by vacuum evaporation and subjected to heating in N2 atmosphere in the temperature range 300°C to 600°C for different durations. After etching Al layer, it has been found that some of the films which are heated around 550°C contain filament like polycrystalline regions surrounding islands of a-Si. This structure has been confirmed through Scanning Electron Mi-croscope(SEM) photographs and electrical conductivity measurements. SEM photographs indicate that, bright regions of amorphous mate­rial are surrounded by dark regions of relatively higher conducting boundaries. The electrical conductivity study shows that there is sharp increase in conductivity of Al doped films, which is attributed to the conduct­ing polycrystalUne filament. A simple model has been proposed to explain the variation of con­ductivity of these transformed films, with process parameters and with temperature. Schottky barrier diodes have been fabricated using these trans­formed materials and their characteristics explained.

Ce travail est consacré au problème de construction des tests d'ajustement dans le cas des processus stochastiques observés en temps continu. Comme modèles d'observations, nous considérons les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. Sous l'hypothèse nulle, nous traitons le cas où chaque modèle dépend d'un paramètre inconnu unidimensionnel et nous proposons l'estimateur de distance minimale pour ce paramètre. Notre but est la construction des tests d'ajustement « asymptotically distribution free » (ADF) de niveau asymtotique α ϵ (0,1) dans le cas de cette hypothèse paramétrique pour les modèles traités. Nous montrons alors que la limite de chaque statistique étudiée ne dépend ni du modèle ni du paramètre inconnu. Les tests d'ajustement basés sur ces statistiques sont donc ADF. L'objectif principal de ce travail est la construction d'une transformation linéaire spéciale. En particulier, nous résolvons l'équation de Fredholm du second type avec le noyau dégénéré. Sa solution nous permet de construire la transformation linéaire désirée. Ensuite, nous montrons que l'application de cette transformation aux statistiques de base étudiées dans chaque modèle nous aide à introduire des statistiques ayant la même limite (l'intégrale du carrée du processus de Wiener). Cette dernière est « distribution free » vu qu'elle ne dépend ni du modèle ni du paramètre inconnu. Par conséquent, nous proposons des tests d'ajustement ADF en se basant sur cette transformation linéaire pour les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. / This work is devoted to the problem of the construction of several goodness of-fit (GoF) tests in the case of somestochastic processes observed in continuous time. As models of observations, we take "small noise" and ergodic diffusionprocesses and an inhomogeneous Poisson process. Under the null hypothesis, we treat the case where each model depends on an unknown one-dimensional parameter and we consider the minimum distance estimator for this parameter. Our goal is to propose "asymptotically distribution free" (ADF) GoF tests of asymptotic size α ϵ (0,1) in the case of the parametric null hypotheses for the considered models. Indeed, we show that the limit of each studied statistic does not depend on the model and the unknown parameter. Therefore, the tests based on these statistics are ADF.The main purpose of this work is to construct a special linear transformation. In particular, we solve Fredholm equation ofthe second kind with degenerated kernel. Its solution gives us the desired linear transformation. Next, we show that theapplication of this transformation to the basic statistics allows us to introduce statistics with the same limit (the integral of the square of the Wiener process). The latter is "distribution free" because it does not depend on the models and the unknown parameter. Therefore, we construct the ADF GoF tests which are based on this linear transformation for the diffusion ("small noise" and ergodic) and inhomogeneous Poisson processes.

L’automobile occupe une place fondamentale dans notre société, au point qu’on a pu parler de « civilisation de l’automobile ». En dépit des critiques qui lui sont régulièrement adressées, celle-ci n’a cessé de se renforcer, avec toujours davantage de voitures par adulte et une proportion croissante de déplacements effectués en voiture. Cependant, depuis le tournant du millénaire, on assiste à un retournement de tendance. Pour la première fois, la mobilité en voiture baisse dans les grandes agglomérations, tandis que la circulation automobile plafonne à l’échelle nationale. Cette évolution, du reste, n’est pas spécifique à la France mais s’observe dans l’ensemble des pays développés, une tendance parfois désignée sous le terme de « peak car (travel) ». Parmi les explications les plus convaincantes de ce retournement, figurent l’augmentation du prix du carburant, suivie de la récession de 2008. La volonté des ménages de maîtriser leurs budgets-temps de transport y contribue également, dans un contexte d’allongement des déplacements vers le travail et de dégradation des vitesses de déplacements. En outre, la diffusion de l’automobile se rapproche de la saturation. Si à long terme, la croissance du kilométrage moyen par adulte est indexée sur le taux de motorisation, cependant à moyen terme l’utilisation des véhicules fluctue en fonction du pouvoir d’achat énergétique, et un modèle basé sur ces deux variables suggère qu’on observerait une réaction normale à une augmentation exceptionnelle du prix du carburant. Les facteurs de croissance du taux de motorisation tiennent eux-mêmes principalement à la succession de générations de plus en plus motorisées, surtout chez les femmes, compte tenu d’un accès de plus en plus large au permis de conduire, à l’activité professionnelle, et d’une urbanisation de plus en plus diffuse, qui ont augmenté le besoin d’une seconde voiture. Pour modéliser l’auto-mobilité, on propose une approche emboîtée, individuelle et longitudinale, segmentée en fonction du genre. L’auto-mobilité peut en effet être vue au niveau individuel comme une succession de choix emboîtés, puisque la détention du permis conditionne l’accès à un véhicule personnel, de même que la motorisation conditionne l’usage d’un véhicule. L’avantage d’une approche longitudinale réside dans la possibilité de distinguer entre mesures d’hétérogénéité et de sensibilité, qui ne sont pas équivalentes. Pour chaque niveau de choix, l’approche est structurée autour d’une analyse de type âge-cohorte-période. Globalement, les taux de motorisation sont plus hétérogènes chez les femmes, un résultat qui est susceptible de recevoir une double interprétation, économique ou sociétale. On peut le voir en termes d’inégalités de genre. Mais il peut également s’interpréter comme le reflet d’un statut encore intermédiaire du second véhicule, dont l’opportunité serait davantage évaluée au regard des besoins et des contraintes réels du ménage. A l’inverse, l’usage des véhicules est à la fois plus élevé et plus hétérogène chez les hommes, compte tenu de la fonction collective du véhicule principal et des arbitrages internes aux ménages quant aux choix du lieu de résidence et des lieux de travail des conjoints. Pour finir, on estime à partir de modèles sur données de panel des effets marginaux et des élasticités par rapport au revenu, au prix du carburant et à la densité, qui sont ensuite comparées avec la littérature. Dans l’ensemble, les résultats sont cohérents avec l’analyse descriptive, ainsi qu’avec la littérature. Le modèle permet également de rendre compte du déclin tendanciel des élasticités, traduisant l’approche de la saturation. Pour finir, une évaluation a posteriori confirme l’opportunité d’une modélisation séquentielle, indiquant que les choix de motorisation sont indépendants des niveaux d’usage de la voiture. / Car ownership and use are a decisive part of our society, which was sometimes designed as the “civilization of the car”. Despite many critics, the car has become ever-more central in the modern way of life, with an ever-increasing number of cars per adult and proportion of trips realized by car. However, from the beginning of the millennium, there was a reversal in the trend towards ever-more car use. For the first time, the average number of daily trips realized by car has been falling down in French conurbations, and nationwide traffic by car is leveling off. This situation, nonetheless, is not specific to France but is common to many developed countries, and is often referred to as the “peak car (travel)”. The main explanations for such a downturn include rising fuel prices from the late 1990’s, followed by the recession in 2008, but also household’s willingness to control their travel time budgets, in a context of increasing commuting distances and reduced travel speeds. Besides, the diffusion of car ownership is approaching saturation. While on the long-run, average car travel per adult is indexed on motorization, mid-term fluctuations of average car use per vehicle are related to the energetic purchasing power, and a simple model based on these two variables is suggesting that the stagnation of car use from the 2000’s could be a reaction of a usual kind to an exceptional rise in fuel prices. The growth in motorization is itself principally caused by the follow-up of ever-more motorized generations, especially among women, given their increasing access to driving license, job participation and ever-more diffuse land use patterns, which have increased the need for a second car within households. In order to model auto-mobility, a nested, individual and longitudinal approach is implemented, segmented by gender. Auto-mobility can indeed be seen as a follow-up of nested choices, as driving license is necessary for holding a car, while access to a personal vehicle is itself required for car use. The advantage of a longitudinal approach consists in the ability to distinguish between measures of heterogeneity and sensitivity, which can be shown not to be equivalent. For every given level of choice, the approach is based on an age-cohort-period-type analysis. Motorization rates happen to be more heterogeneous among women, a result which is likely to receive an interpretation either of a social or economic nature. According to the first interpretation, it should be regarded as the illustration of gender inequalities. However, it could also be regarded as reflecting the still-intermediary status of the second vehicle, which opportunity is assessed depending upon household’s specific needs and constraints. On the contrary, car use is at the same time higher and more heterogeneous among men, given the collective function of the first vehicle and household’s internal trade-offs in residential and job choices. Finally, average partial effects and elasticities are estimated from panel data models, either with respect to income, fuel prices or density. Generally, results are consistent with the descriptive part, as with the literature. The model also rationally gives account of the decreasing trend for elasticities, which was often noticed in the literature and reflects the approach of saturation. As a conclusion, an a posteriori evaluation of the assumption of a sequential decision process is made, confirming that choices of motorization and car use are mutually independent.

Jump-diffusion processes often model financial time series as they can simulate the random jumps that they frequently exhibit. These jumps can be seen as anomalies and are essential for financial analysis and model building, making them vital to detect.The realized variation, realized bipower variation, and realized semi-variation were tested to see if one could use them to detect jumps in a jump-diffusion process and if anomaly detection algorithms can use them as features to improve their accuracy. The algorithms tested were Isolation Forest, Robust Random Cut Forest, and Isolation Forest Algorithm for Streaming Data, where the latter two use streaming data. This was done by generating a Merton jump-diffusion process with a varying jump-rate and tested using each algorithm with each of the features. The performance of each algorithm was measured using the F1-score to compare the difference between features and algorithms. It was found that the algorithms were improved from using the features; Isolation Forest saw improvement from using one, or more, of the named features. For the streaming algorithms, Robust Random Cut Forest performed the best for every jump-rate except the lowest. Using a combination of the features gave the highest F1-score for both streaming algorithms. These results show one can use these features to extract jumps, as anomaly scores, and improve the accuracy of the algorithms, both in a batch and stream setting. / Hopp-diffusionsprocesser används regelbundet för att modellera finansiella tidsserier eftersom de kan simulera de slumpmässiga hopp som ofta uppstår. Dessa hopp kan ses som anomalier och är viktiga för finansiell analys och modellbyggnad, vilket gör dom väldigt viktiga att hitta. Den realiserade variationen, realiserade bipower variationen, och realiserade semi-variationen är faktorer av en tidsserie som kan användas för att hitta hopp i hopp-diffusionprocesser. De används här för att testa om anomali-detektionsalgoritmer kan använda funktionerna för att förbättra dess förmåga att detektera hopp. Algoritmerna som testades var Isolation Forest, Robust Random Cut Forest, och Isolation Forest Algoritmen för Strömmande data, där de två sistnämnda använder strömmande data. Detta gjordes genom att genera data från en Merton hopp-diffusionprocess med varierande hoppfrekvens där de olika algoritmerna testades med varje funktion samt med kombinationer av funktioner. Prestationen av varje algoritm beräknades med hjälp av F1-värde för att kunna jämföra algoritmerna och funktionerna med varandra. Det hittades att funktionerna kan användas för att extrahera hopp från hopp-diffusionprocesser och även använda de som en indikator för när hopp skulle ha hänt. Algoritmerna fick även ett högre F1-värde när de använde funktionerna. Isolation Forest fick ett förbättrat F1-värde genom att använda en eller fler utav funktionerna och hade ett högre F1-värde än att bara använda funktionerna för att detektera hopp. Robust Random Cut Forest hade högst F1-värde av de två algoritmer som använde strömmande data och båda fick högst F1-värde när man använde en kombination utav alla funktioner. Resultatet visar att dessa funktioner fungerar för att extrahera hopp från hopprocesser, använda dem för att detektera hopp, och att algoritmernas förmåga att detektera hoppen ökade med hjälp av funktionerna.

The concept of Sustainable Forest Management (SFM) has been promoted in the past few decades all over the world. Non-industrial private forest (NIPF) owners play an important role in that aspect in the U.S. because of their number (about 16 millions), the size of forest land under their control (about half of all forest land in the continental US), and the dynamism of their population (increasing number of new owners). This study sought to better understand how NIPF owners come to a decision for adoption (or non-adoption) of SFM practices. We developed a theoretical model combining four theories (the Value-Belief-Norm theory, the Theory of Planned Behavior, the Elaboration Likelihood Model, and the Innovation-Diffusion Process) to explain NIPF's decision making. Using multivariate analyses, we determined which elements of the developed theoretical model were significant in explaining adoption of eight groups of practices. Overall, some of the most significant predictors of adoption we identified were technical assistance, motivations for owning land and the use of a written management plan. Particular attention was also directed toward the eventual relationship between education and adoption of SFM practices and it was found that NIPF owners who attended educational programs tended to be likely adopters compared to those who did not attend any educational program. Since SFM was not limited to the US, we also analyzed the concept of SFM with the same goals as in the US, but under a completely different context (socio-cultural, economic and ecologic) in Africa, through the community-based natural resource management (CBNRM) system. We used four case studies and focused on criteria such as participation, equity (both procedural and distributive, power devolution, trust, etc) to analyze how CBNRM works on the field, what lessons to take from the cases to better ensure the goal of sustainability of the resources. / Ph. D.