Exit-time problem for self-interacting and self-stabilizing diffusion processes
Speaker: Ashot Aleksian, Jean Monnet University, France.
Keywords: Self-interacting diffusion, self-stabilizing diffusion, McKean-Vlasov process, exit-time, Kramers’ law, Freidlin-Wentzell theory,
metastability, large deviations.
Summary: In this talk the work done by the author within the framework of his PhD thesis is presented. Namely, we first discuss the exit-time problem: its formulation and
existing results in the case of the Itô diffusion (known under the name of Freidlin-Wentzell theory). Then, two main processes of interest are presented: self-interacting (SID) and
self-stabilizing (SSD) diffusion processes. Both processes are characterized by including a certain interaction in the drift term. In the case of SID, the process
trajectorially interacts with its own path. For SSD, the interaction includes convolution with the law of the process at each point of time (particular case of
McKean-Vlasov process). Exit-time results for SID and SSD, obtained by the author in collaboration with Pierre Del Moral, Aline Kurtzmann, and Julian Tugaut, are presented.
Comparison with previously known results is provided. Special attention to the methods used to resolve exit-time problem in the case of SSD is paid.
This work is based on the following papers:
1. Ashot Aleksian, Pierre Del Moral, Aline Kurtzmann, and Julian Tugaut.
Self-interacting diffusions: long-time behaviour and exit-problem in the
convex case, 2023 [to appear in ESAIM: PS] ArXiv:
arxiv.org/abs/2303.14997
2. Ashot Aleksian, Aline Kurtzmann, and Julian Tugaut. Exit-problem for a
class of non-Markov processes with path dependency, 2023 [Preprint.]
ArXiv: arxiv.org/abs/2306.08706
as well as the PhD thesis done by the author under the supervision of Aline
Kurtzmann, and Julian Tugaut.
Research Seminar "Stochastic Analysis and its Applications in Economics"
Academic supervisors: Alexander Kolesnikov, Valentin Konakov
Language: English
Научно-исследовательский семинар "Стохастический анализ и его применения в экономике"
Преподаватели: Колесников Александр Викторович, Конаков Валентин Дмитриевич
Язык: английский