Exponential Convergence of Non-Linear Monotone SPDEs

2013/10/30 by Feng‐Yu Wang, Wang, Feng-Yu
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1310.7997

openalex publication_date 2013/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Markov semigroup P_t with invariant probability measure μ, a constant ≪>0 is called a lower bound of the ultra-exponential convergence rate of P_t to μ, if there exists a constant C∈ (0,∞) such that sup_{μ(f²)≤ 1}‖P_tf-μ(f)‖_∞ ≤ C \e^{-≪ t}, t≥ 1. By using the coupling by change of measure in the line of [F.-Y. Wang, Ann. Probab. 35(2007), 1333--1350], explicit lower bounds of the ultra-exponential convergence rate are derived for a class of non-linear monotone stochastic partial differential equations. The main result is illustrated by the stochastic porous medium equation and the stochastic p-Laplace equation respectively. Finally, the V-uniformly exponential convergence is investigated for stochastic fast-diffusion equations.

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