This thesis is concerned with certain properties of stochastic growth models. A stochastic growth model is a model of infection spread, through a population of individuals, that incorporates an element of randomness. The models we consider are variations on the contact process, the simplest stochastic growth model with a recurrent infection. Three main examples are considered. The first example is a version of the contact process on the complete graph that incorporates dynamic monogamous partnerships. To our knowledge, this is the first rigorous study of a stochastic spatial model of infection spread that incorporates some form of social dynamics. The second example is a non-monotonic variation on the contact process, taking place on the one-dimensional lattice, in which there is a random incubation time for the infection. Some techniques exist for studying non-monotonic particle systems, specifically models of competing populations [38] [12]. However, ours is the first rigorous study of a non-monotonic stochastic spatial model of infection spread. The third example is an additive two-stage contact process, together with a general duality theory for multi-type additive growth models. The two-stage contact process is first introduced in \cite{krone}, and several open questions are posed, most of which we have answered. There are many examples of additive growth models in the literature [26] [16] [29] [49], and most include a proof of existence of a dual process, although up to this point no general duality theory existed. In each case there are three main goals. The first is to identify a phase transition with a sharp threshold or ``critical value'' of the transmission rate, or a critical surface if there are multiple parameters. The second is to characterize either the invariant measures if the population is infinite, or to characterize the metastable behaviour and the time to extinction of the disease, if the population is finite. The final goal is to determine the asymptotic behaviour of the model, in terms of the invariant measures or the metastable states. In every model considered, we identify the phase transition. In the first and third examples we show the threshold is sharp, and in the first example we calculate the critical value as a rational function of the parameters. In the second example we cannot establish sharpness due to the lack of monotonicity. However, we show there is a phase transition within a range of transmission rates that is uniformly bounded away from zero and infinity, with respect to the incubation time. For the partnership model, we show that below the critical value, the disease dies out within C log N time for some C>0, where N is the population size. Moreover we show that above the critical value, there is a unique metastable proportion of infectious individuals that persists for at least e^{\gamma N}$ time for some $\gamma>0$. For the incubation time model, we use a block construction, with a carefully chosen good event to circumvent the lack of monotonicity, in order to show the existence of a phase transition. This technique also guarantees the existence of a non-trivial invariant measure. Due to the lack of additivity, the identification of all the invariant measures is not feasible. However, we are able to show the following is true. By rescaling time so that the average incubation period is constant, we obtain a limiting process as the incubation time tends to infinity, with a sharp phase transition and a well-defined critical value. We can then show that as the incubation time approaches infinity (or zero), the location of the phase transition in the original model converges to the critical value of the limiting process (respectively, the contact process). For the two-stage contact process, we can show that there are at most two extremal invariant measures: the trivial one, and a non-trivial upper invariant measure that appears above the critical value. This is achieved using known techniques for the contact process. We can show complete convergence, from any initial configuration, to a combination of these measures that is given by the survival probability. This, and some additional results, are in response to the questions posed by Krone in his original paper \cite{krone} on the model. We then generalize these ideas to develop a theory of additive growth models. In particular, we show that any additive growth model, having any number of types and interactions, will always have a dual process that is also an additive growth model. Under the additional technical condition that the model preserves positive correlations, we can then harness existing techniques to conclude existence of at most two extremal invariant measures, as well as complete convergence. / Graduate

Dans cette thèse nous examinons différents aspects des fluctuations dans les économies émergentes. Premièrement, afin d’établir les régularités empiriques de ces pays nous examinons le contexte économique des pays du Moyen Orient et d’Afrique du Nord. Ensuite, nous estimons un modèle des cycles réels pour essayer de reproduire les faits stylisés de ces pays, mais aussi pour évaluer la performance de ces modèles néoclassiques augmentés de deux types de chocs de productivité transitoire et permanent. Ceci fait l’objet du chapitre 2 dont le résultat est en faveur de l'hypothèse "Le cycle c'est la tendance" . Le deuxième aspect porte sur l’importance des frictions financières, il est traité dans le troisième chapitre qui introduit des chocs financiers au modèle de croissance stochastique. Nous identifions le rôle des frictions financières dans l’économie tunisienne comme étant un amplificateur de l’effet des chocs de productivité. Le quatrième chapitre porte sur l'analyse de la politique monétaire. Premièrement, nous examinons le régime de ciblage d’inflation où nos résultats empiriques supportent une implémentation de la stricte version du ciblage d’inflation avec une fonction de réaction basée sur des prévisions de l'inflation. Deuxièmement, nous exploitant les règles monétaires optimales en présence de la rigidité d l'information dans le cadre d’un modèle stochastique d’équilibre général (DSGE). Nos résultats, révèlent que les chocs du taux de marge de la force de travail jouent un rôle important dans les fluctuations de l’économie tunisienne, la règle de Taylor produit un taux satisfaisant de bien être, alors que les règles qui ciblent le niveau de prix ne sont pas efficaces. / This thesis investigates different aspects of the fluctuations in emerging economies. First, it examines the MENA countries’ context to establish the empirical regularities. Then, to replicate the MENA countries’ business cycle patterns observed in the annual data, we estimate a standard real business cycle (RBC) model to assess the performance of the neoclassical model with transitory and permanent shocks. This is the purpose of chapter 2 which results support the assumption "The cycle is the trend". The second aspect refers to the importance of financial frictions and is addressed in the third chapter which adds new financial shocks to the stochastic growth model. We determine the role of financial frictions in the Tunisian economy not as the source of business cycle fluctuations but as an amplifier of the effects of total factor of productivity shocks.The fourth chapter analyzes monetary policy in emerging economies. Firstly, we examine the inflation targeting regime under the lens of a New Keynesian forward-looking model. We also, estimate a Taylor rule and some other alternatives in order to determine which rule to adopt within this framework. Empirical results support the implementation of a strict inflation targeting regime, with an inflation forecast based rule as a reaction function. Secondly, we explore the optimal monetary policy rules using a New Keynesian DSGE model. In particular we assume that information stickiness as the only type of rigidity in the model. We find that Whereas, Taylor rule in its original version provides substantial welfare gains, price-level targeting regime was suboptimal.

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.

A wide majority of orchid populations are decreasing due to habitat fragmentation and to changes in land management. Population size, density and habitat quality are factors that are expected to be positively related to the viability and future growth of a population. We evaluated if population size, density and soil organic matter were good predictors of growth, survival, flowering, recruitment, and growth rate in 18 populations of the long-lived orchid Gymnadenia conopsea. We followed the populations for four years. Recruitment in 2020 increased with population size, and survival in 2018 was higher in denser populations. However, flowering probability and number of flowers both decreased with population size in 2018. Soil organic matter did not significantly influence any vital rate. In total, the studied population factors could explain very little of the variation in demography. The matrix modelling showed that 14 of the 18 populations had a positive stochastic growth rate, even with an increased probability of summer drought (scenario with 50% of the years equal to the dry summer of 2018). In the populations with negative growth rate, the probability of quasi-extinction in the next 50 years varied from 90 to 100%. Declining populations were characterized by low survival following the dry year. In sum, population size, density and soil organic matter did not convincingly explain variation in growth rate of G. conopsea, suggesting that other environmental factors are responsible of governing variation in vitals rates and population dynamics.

In this thesis, I combined comparative and experimental approaches to examine selection on reproductive traits and population differentiation in the insect-pollinated, self-incompatible, perennial herb Primula farinosa. More specifically, I (1) determined whether the effects of floral display and interactions with pollinators and seed predators, and plant reproductive success were frequency-dependent and affected by surrounding vegetation context, (2) examined the consequences of intermittent drought years on population dynamics using numerical simulations based on demographic data collected over seven years, (3) analyzed among-population differentiation in flowering phenology and reproductive allocation, and its relationship to soil-depth at the site of origin. A field experiment suggested that conspicuous plants facilitate inconspicuous plants in terms of pollinator attraction, and that the facilitation effect is contingent on the height of the surrounding vegetation. Further experiments revealed that both mutualistic and antagonistic interactions can result in frequency-dependent selection on floral display. Among inconspicuous plants, both fruit initiation, and damage from seed predators increased with the proportion of the conspicuous morph. The relative strength of these effects, and therefore their net outcome on the relationship between morph ratio and seed production varied among years. I combined information on vital rates and their relation to environmental conditions in simulations to predict future population viability in changing environments. Simulated stochastic population growth rate decreased with increasing frequency of drought years. Reproductive allocation varied significantly among populations both in the field and in a common-garden experiment, but was correlated with soil depth at the site of origin only in the field. The results suggest that among-population variation in reproductive effort in the field mainly reflects plastic responses to environmental conditions, and that this plasticity may be adaptive. The common-garden experiment suggested that the study populations have diverged genetically in flowering time.

<p>In this thesis, I combined comparative and experimental approaches to examine selection on reproductive traits and population differentiation in the insect-pollinated, self-incompatible, perennial herb <i>Primula farinosa</i>. More specifically, I (1) determined whether the effects of floral display and interactions with pollinators and seed predators, and plant reproductive success were frequency-dependent and affected by surrounding vegetation context, (2) examined the consequences of intermittent drought years on population dynamics using numerical simulations based on demographic data collected over seven years, (3) analyzed among-population differentiation in flowering phenology and reproductive allocation, and its relationship to soil-depth at the site of origin. </p><p>A field experiment suggested that conspicuous plants facilitate inconspicuous plants in terms of pollinator attraction, and that the facilitation effect is contingent on the height of the surrounding vegetation. Further experiments revealed that both mutualistic and antagonistic interactions can result in frequency-dependent selection on floral display. Among inconspicuous plants, both fruit initiation, and damage from seed predators increased with the proportion of the conspicuous morph. The relative strength of these effects, and therefore their net outcome on the relationship between morph ratio and seed production varied among years. </p><p>I combined information on vital rates and their relation to environmental conditions in simulations to predict future population viability in changing environments. Simulated stochastic population growth rate decreased with increasing frequency of drought years. </p><p>Reproductive allocation varied significantly among populations both in the field and in a common-garden experiment, but was correlated with soil depth at the site of origin only in the field. The results suggest that among-population variation in reproductive effort in the field mainly reflects plastic responses to environmental conditions, and that this plasticity may be adaptive. The common-garden experiment suggested that the study populations have diverged genetically in flowering time.</p>

L’objectif de cette thèse est de mieux appréhender les déterminants du risque souverain et de la soutenabilité budgétaire des pays émergents, afin d’identifier les éléments qui permettraient à ces pays de se protéger d’un tel risque. Nous mettons en place des outils économétriques et théoriques adaptés aux particularités de ces pays. Ces derniers sont ensuite déclinés pour tenter d’anticiper les épisodes de défaut souverain sévère via un modèle à changement de régime de type "early warning", pour effectuer des simulations stochastiques de ratio de dette souveraine à moyen-terme et évaluer les effets de politiques budgétaires définies à cet horizon et enfin, pour caractériser la distribution du ratio de dette externe de ces pays. Cette thèse entend ainsi identifier les pays qui semblent les plus exposés au risque souverain et définir des recommandations de politique économique qui prennent en compte l’hétérogénéité au sein du «bloc» des pays émergents et au cours du temps. / The objective of this thesis is to obtain a better understanding of the determinants of sovereign default and medium-term sustainability inemerging market countries, so as to define ways through which they may protect themselves from these sovereign risks. We provide econometric tools and a theoretical model that are adapted to these countries’ specific features. This aims to anticipate severe sovereign default episodes through a regime switching early-warning type model, to assess medium-term public debt prospects and the impact of defined fiscal policies through stochastic debt simulations and to characterize the distribution of the external debt ratio of emerging market countries. It eventually enables to identify the countries that are the most exposed to sovereign risk and to draw up a set of policy recommendations, allowing for a differentiation within this heterogeneous block of countries and through time.