Université de Neuchâtel

Persistance de processus de Markov déterministes par morceaux

Strickler, Edouard Antoine ; Benaïm, Michel (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2019.

This thesis is devoted to the study of the long-term behaviour of Piecewise Deterministic Markov Processes (PDMP). That is, a process (Xt,It)t≥0 living in ℝd × E with E a finite space, where X is continuous and evolves between the jumps of I as dXt / dt = FIt (Xt),...

Université de Neuchâtel

Long term behaviour of self-interacting diffusions

Gauthier, Carl-Erik Robert Reimer ; Benaïm, Michel (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2016.

The purpose of this thesis is the study of the long term behaviour of Self-Interacting Diffusions on compact Riemannian manifolds solving formally the stochastic differential equation $$dX_t =dB_t(X_t)- \nabla V_t(X_t)dt, $$ with $V_t(x)= \int_0^t V(x,X_s)ds$ and $$V(x,y)=\sum_{k=1}^n a_k e_k(x)e_k(y),\; a_k\neq 0.$$ When all coefficients are positive, the particle tends to go as far as...

Université de Neuchâtel

Long time behavior of stochastic population models

Marmet, Bastien ; Benaïm, Michel (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2014.

The object of this thesis is the study of the asymptotic behavior of two classes of stochastic population models that both can be viewed as small random perturbations of a deterministic population dynamic. The first of these models is a discrete time Markov chain modeling the evolution of a population game with N players and d types. The second model is a constrained diffusion process modeling...

Université de Neuchâtel

Algorithmes d'approximation stochastiques et inclusions différentielles

Roth, Gregory ; Benaïm, Michel (Dir.) ; Frankowska, Hélène (Codir.) ; Schlenk, Felix (Codir.) ; Sorin, Sylvina (Codir.) ; Tarrès, Pierre (Codir.)

Thèse de doctorat : Université de Neuchâtel, 2011.

A successful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Benaïm, Hofbauer and Sorin generalised this approach to stochastic approximation algorithms whose average behavior is related to a differential inclusion instead. The aim of this thesis is...

Université de Neuchâtel

Persistance en environnements fluctuants

Atchadé, Kolawolé Akansa Sourou ; Benaïm, Michel (Dir.)

Thèse de doctorat : Université de Neuchâtel, 2011 ; 2185.

To understand better how biotic factors and environmental fluctuations affect the maintenance of species diversity in a population, we develop a mathematical theory of coexistence, extending non-linear theory of permanence to stochastic difference and differential equations. Our condition for species coexistence requires that there is a fixed weight vector such that the associated linear convex...