Limit behavior of the invariant measure for Langevin~dynamics

• Autorzy: Barrera Gerardo

Identyfikatory

DOI

10.37190/0208-4147.00020

• Języki publikacji: EN

Abstrakty

EN

We consider the Langevin dynamics on R^d with an overdamped vector field and driven by multiplicative Brownian noise of small amplitude √ϵ, ϵ>0. Under suitable assumptions on the vector field and the diffusion coefficient, it is well-known that it has a unique invariant probability measure μ ^ϵ . We prove that as ε tends to zero, the probability measure ϵ^d/2μ ^ϵ(√ϵdx) converges in the p--Wasserstein distance for p∈[1,2] to a Gaussian measure with zero-mean vector and non-degenerate covariance matrix which solves a Lyapunov matrix equation. Moreover, the error term is estimated. We emphasize that generically no explicit formula for μ^ϵ can be found.

Słowa kluczowe

EN

coupling; Gaussian distribution; invariant distribution; Langevin dynamics; Ornstein-Uhlenbeck process; perturbations of dynamical systems; Wasserstein distance

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 1
• Strony: 143--162
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Barrera Gerardo

• Department of Mathematical and Statistical Sciences, University of Helsinki, PL 68, Pietari Kalmin katu 5, Postal Code: 00560. Helsinki, Finland

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