Talagrand Inequality on Free Path Space and Application to Stochastic Reaction Diffusion Equations

Abstract

By using a split argument due to [1], the transportation cost inequality is established on the free path space of Markov processes. The general result is applied to stochastic reaction diffusion equations with random initial values.

Transportation Inequalities Under Uniform Metric for a Stochastic Heat Equation Driven by Time-White and Space-Colored Noise

“…Applying Proposition 2.3 and Theorem 3.1 and using the same approach in the proof of [27,Theorem 3.1], we can get the following transportation inequality for the stochastic heat equation with random initial values, whose proof is omitted here. Corollary 3.2.…”

“…Recently, F.-Y. Wang and T. Zhang [27] studied the transportation inequalities for SPDEs with random initial values.…”

Talagrand’S Transportation Inequality for Spdes with Locally Monotone Drifts

“…F.-Y. Wang and T. Zhang [37] studied the T 2 pCq for SPDEs with random initial values. Y. Li and X. Wang [19] established the T 2 pCq w.r.t.…”

TCI for SDEs with irregular drifts

“…It is worth noting that most of the above references of TCIs for solutions to SDEs and SFDEs are required to meet Lipschitz condition for the drifts, some references relaxed this condition to the case with one-sided Lipschitz condition. Motivated by [16,17], the goal of this paper is to establish the equivalent expressions of Wasserstein distance and relative entropy of measures defined on a polish space by introducing a Homeomorphism on it, which implies the equivalent expression of T p (C) for laws of solutions to two equivalent SDEs, the coefficients of one SDE are singular.…”