Diffusion Approximation for Transport Equations with Dissipative Drifts
Probability
2022-05-05 v1 Dynamical Systems
Abstract
We study stochastic differential equations(SDEs) with a small perturbation parameter. Under the dissipative condition on the drift coefficient and the local Lipschitz condition on the drift and diffusion coefficients we prove the existence and uniqueness result for the perturbed SDE, also the convergence result for the solution of the perturbed system to the solution of the unperturbed system when the perturbation parameter approaches zero.We consider the application of the above-mentioned results to the Cauchy problem and the transport equations.
Cite
@article{arxiv.2205.01750,
title = {Diffusion Approximation for Transport Equations with Dissipative Drifts},
author = {Luca Di Persio and Yuri Kondratiev and Viktorya Vardanyan},
journal= {arXiv preprint arXiv:2205.01750},
year = {2022}
}