Non uniqueness of stationary measures for self-stabilizing processes

Autor: Tugaut, Samuel Herrmann Julian

We investigate the existence of invariant measures for self-stabilizing diffusions. These stochastic processes represent roughly the behavior of some Brownian particle moving in a double-well landscape and attracted by its own law. This specific self

Externí odkaz: http://arxiv.org/abs/0903.2460

Approximation of exit times for one-dimensional linear diffusion processes

Autor: Samuel Herrmann, Nicolas Massin

Publikováno v: Computers & Mathematics with Applications
Computers & Mathematics with Applications, Elsevier, 2020, 80 (6), pp.1668-1682. ⟨10.1016/j.camwa.2020.07.023⟩

International audience; In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck con

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::02041f432de2e59169508478b5838e04
https://doi.org/10.1016/j.camwa.2020.07.023

The walk on moving spheres: A new tool for simulating Brownian motion’s exit time from a domain

Autor: Sylvain Maire, Samuel Herrmann, Madalina Deaconu

Publikováno v: Mathematics and Computers in Simulation
9th IMACS Seminar on Monte Carlo Methods (MCM)
9th IMACS Seminar on Monte Carlo Methods (MCM), Jul 2013, Annecy le Vieux, France. pp.28-38, ⟨10.1016/j.matcom.2015.07.004⟩
9th IMACS Seminar on Monte Carlo Methods (MCM), Jul 2013, Annecy le Vieux, France. ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS, 135, pp.28-38, 2017, 〈http://www.sciencedirect.com/science/article/pii/S0378475415001366〉. 〈10.1016/j.matcom.2015.07.004〉
Mathematics and Computers in Simulation, Elsevier, 2017, 135, pp.28--38. 〈https://doi.org/10.1016/j.matcom.2015.07.004〉

International audience; In this paper we introduce a new method for the simulation of the exit time and exit position of a (delta-dimensional Brownian motion from a domain. The main interest of our method is that it avoids splitting time schemes as w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8781f62c40913e40e1ffd61bc87e26cd
https://doi.org/10.1016/j.matcom.2015.07.004

Simulation of hitting times for Bessel processes with non-integer dimension

Autor: Madalina Deaconu, Samuel Herrmann

Publikováno v: Bernoulli
Bernoulli, 2017, 23 (4B), pp.3744-3771. ⟨10.3150/16-BEJ866⟩
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3744-3771. ⟨10.3150/16-BEJ866⟩
Bernoulli 23, no. 4B (2017), 3744-3771
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3744-3771. 〈10.3150/16-BEJ866〉

International audience; In this paper, we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neuroscience

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5fc438af9de2ed1a8a3cef5c4d867320
https://hal.science/hal-00933198v2/file/HAL-version2.pdf

Initial-boundary value problem for the heat equation - A stochastic algorithm

Autor: Samuel Herrmann, Madalina Deaconu

Publikováno v: Annals of Applied Probability
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), In press
Annals of Applied Probability, 2018, 28 (3), pp.1943-1976. ⟨10.1214/17-AAP1348⟩
Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2018, 28 (3), pp.1943-1976. ⟨10.1214/17-AAP1348⟩
Ann. Appl. Probab. 28, no. 3 (2018), 1943-1976

International audience; The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introdu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c08debdfda361b716924957888673405
https://hal.archives-ouvertes.fr/hal-01380365/file/space-time-dirichlet-HAL.pdf