Exponential convergence to a quasi-stationary distribution and applications

Abstract

This HDR is a reflection of my research since the end of my PhD thesis. It is also a presentation, in a more accessible form than in the original works, of the main theoretical tools developed during this time, as well as their application to various models. This work focuses on the study of the quasi-stationary behavior of absorbed processes and their applications. In particular, I have focused on developing sufficient criteria for the existence and convergence of the conditional laws of a process towards a quasi-stationary distribution. These results have consequences that go beyond the theory of quasi-stationary distributions and lead naturally to the study of their applications to quasi-ergodic properties, to the R-positivity of unbounded semi-groups, to the study of measured value Pólya processes and self-reinforced processes. Finally, other studies will be exposed, some of which have lead me to co-supervise research internships, a PhD thesis and a post-doctorate.

Publication
(Habilitation à diriger des recherches)
Denis Villemonais
Denis Villemonais
Assistant professor in Applied Mathematics - Membre junior IUF