Ashot Aleksian | Toulouse School of Economics

About Me

I am Ashot Aleksian, post-doctoral researcher at Toulouse School of Economics in Toulouse, France.

Research Interests

Probability theory and stochastic analysis. In particular:

Stochastic Processes: Itô diffusion, McKean-Vlasov process, Self-interacting diffusion.
Metastability, exit-problem, Freidlin-Wentzell theory, Large Deviations Theory.

Publications

Exit-problem for Self-interacting and Self-stabilizing Diffusion Processes

Ashot Aleksian

PhD thesis, 2023.

HAL
Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times

Ashot Aleksian, and Julian Tugaut

Electron. J. Probab. 29: 1-31 (2024).

pdf
preprint

Exit-problem for a class of non-Markov processes with path dependency

Ashot Aleksian, Aline Kurtzmann, and Julian Tugaut

on revision for PTRF, 2023.

arXiv
Self-interacting diffusions: Long-time behaviour and exit-problem in the uniformly convex case

Ashot Aleksian, Pierre Del Moral, Aline Kurtzmann, and Julian Tugaut

ESAIM: PS 28 (2024) 46–61.

pdf

News

[Nov. 2024] A talk on the "LSA Winter meeting" workshop in HSE university Moscow, Russia
[Sep. 2024] Our paper "Measure-dependent non-linear diffusions with superlinear drifts: asymptotic behaviour of the first exit-times" is now published in Electron. J. Probab.
[June 2024] I gave a talk "Exit-time problem for some non-Markovian diffusion processes" on "Journées de Probabilités 2024" in Bordeaux, France.
[June 2024] A presentation on the TSE doctoral workshop in Toulouse, France.
[Apr. 2024] A talk titled "Exit-time for McKean-Vlasov processes: beyond the convex case" at the seminar of the SPOC team at Institut de Mathématiques de Bourgogne in Dijon, France.
[Mar. 2024] I presented recently obtained results in a talk titled "Exit-time for McKean-Vlasov processes: beyond the convex case" at the research seminar of the Probabilités, Analyse et Statistique team at Clermont Auvergne University, Clermont-Ferrand, France.
[Feb. 2024] I gave a talk titled "Metastability for non-linear processes: new results and open questions" at the research seminar of the Probability team at IRMAR Institut in Rennes, France.
[Feb. 2024] A talk titled "Metastability for non-linear processes" that I gave at the research seminar of the ProbaStat team at Poitiers, France.
[Nov. 2023] Start of a post-doctoral research position at Toulouse School of Economics (TSE) in Toulouse, France.
[Nov. 2023] I successfully defended my PhD thesis entitled “Exit-problem for Self-interacting and Self-stabilizing Diffusion Processes”. See the full text here.
[Oct. 2023] We finished a paper showing Kramers' type law and the exit-location result for McKean-Vlasov diffusion process in multi-well landscape with generalazied interaction term. Preprint can be found here.
[Oct. 2023] A talk presenting the work done within the framework of the PhD thesis on the online research seminar "Stochastic Analysis and Applications" organized by the Laboratory of Stochastic Analysis and its Applications of HSE Moscow, Russia.
[Sept. 2023] Poster presentation on the conference "A Random Walk in the Land of Stochastic Analysis and Numerical Probability" in Marseille, France.
[June 2023] We finished a paper on the exit-time and exit-location problems for self-interacting diffusions in general case. Preprint can be found here.
[June 2023] Presentation of the new results about the exit-problem for self-interacting diffusion in general case on the workshop "Stochastic processes, metastability and applications" in Nancy, France.
[Mar. 2023] We finished a paper solving the exit-problem for self-interacting diffusion in the case of convex confinement and interaction. Preprint can be found here.
[Oct. 2022] Presentation on the exit-time probelem on "First Franco-Japanese workshop on chemotaxis models (macroscopic and microscopic viewpoints)" in Sendai, Japan.
[May 2022] Presentation on the workshop "Metastability, mean-field particle systems and nonlinear processes" in Saint-Étienne, France.
[Apr. 2021] Start of the Sakura (Hubert Curien Program) project together with Kentaro Fujie, Milica Tomasevic, Julian Tugaut, and Hiroshi Wakui.