Transportation Cost Inequality on Path Spaces with Uniform Distance

Abstract

Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in Let $M$beacompleteRiemnnianmanifoldand$μ$thedistributionofthediffusionprocessgeneratedby$\ff 1 2\DD+Z$where$Z$isa$C^1$-vectorfield.When$\Ric-\nn Z$isboundedbelowand$Z$has,forinstance,lineargrowth,thetransportation-costinequalitywithrespecttotheuniformdistanceisestablishedfor$μ$onthepathspaceover$M$. A simple example is given to show the optimality of the condition.

to appear in Stochastic Processes and Applications

References in corpus (1)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions