Convergence Rate for Degenerate Partial and Stochastic Differential Equations via weak Poincar\'e Inequalities
Probability
2021-10-13 v1 Functional Analysis
Abstract
We employ weak hypocoercivity methods to study the long-term behavior of operator semigroups generated by degenerate Kolmogorov operators with variable second-order coefficients, which solve the associated abstract Cauchy problem. We prove essential m-dissipativity of the operator, which extends previous results and is key to the rigorous analysis required. We give estimates for the -convergence rate by using weak Poincar\'e inequalities. As an application, we obtain estimates for the (sub-)exponential convergence rate of solutions to the corresponding degenerate Fokker-Planck equations and of weak solutions to the corresponding degenerate stochastic differential equation with multiplicative noise.
Keywords
Cite
@article{arxiv.2110.05536,
title = {Convergence Rate for Degenerate Partial and Stochastic Differential Equations via weak Poincar\'e Inequalities},
author = {Alexander Bertram and Martin Grothaus},
journal= {arXiv preprint arXiv:2110.05536},
year = {2021}
}