Transportation Cost Inequalities for Neutral Functional Stochastic Equations

TL;DR

This paper establishes transportation cost inequalities for neutral functional stochastic differential equations using Girsanov transformation and martingale representation, covering both path space distances and extending to stochastic PDEs.

Contribution

It introduces new transportation cost inequalities for neutral functional stochastic equations and their partial differential counterparts, utilizing advanced probabilistic techniques.

Findings

Transportation inequalities established for neutral functional stochastic equations.

Results apply to both uniform and L^2 distances on path space.

Extension of inequalities to stochastic partial differential equations.

Abstract

By using Girsanov transformation and martingale representation, Talagrand-type transportation cost inequalities, with respect to both the uniform and the $L^2$ distances on the global free path space, are established for the segment process associated to a class of neutral functional stochastic differential equations. Neutral functional stochastic partial differential equations are also investigated.