2023/06/14 by Ashot Aleksian, Aleksian, Ashot, Aline Kurtzmann +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60F10 #60H10 #60K35 #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2306.08706
openalex publication_date 2023/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
We study the exit-time of a self-interacting diffusion from an open domain G ⊂ ℝd. In particular, we consider the equation dXt = - ( ∇ V(Xt) + (1)/(t)∫0t∇ F (Xt - Xs)ds ) dt + σdWt. We are interested in the small-noise (σ→ 0) behaviour of the exit-time from the potentials' domain of attraction. In this work rather weak assumptions on the potentials V and F, and on the domain G are considered. In particular, we do not assume V nor F to be either convex or concave, which covers a wide range of self-attracting and self-repelling stochastic processes possibly moving in a complex multi-well landscape. The Large Deviation Principle for the Self-interacting diffusion with generalized initial conditions is established. The main result of the paper states that, under some assumptions on the potentials V and F, and on the domain G, the Kramers' type law for the exit-time holds. Finally, we provide a result concerning the exit-location of the diffusion.