Transportation Cost Inequality on Path Spaces with Uniform Distance

Shizan Fang; Feng-Yu Wang; Bo Wu

paper

Transportation Cost Inequality on Path Spaces with Uniform Distance

arXiv:0712.3139

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 $b e a co m pl e t e R i e mnnianmani f o l d an d$ μ $t h e d i s t r ib u t i o n o f t h e d i f f u s i o n p r ocess g e n er a t e d b y$ \ff 1 2\DD+Z $w h er e$ Z $i s a$ C^1 $- v ec t or f i e l d . W h e n$ \Ric-\nn Z $i s b o u n d e d b e l o w an d$ Z $ha s, f or in s t an ce, l in e a r g r o w t h, t h e t r an s p or t a t i o n - cos t in e q u a l i t y w i t h r es p ec tt o t h e u ni f or m d i s t an ce i ses t ab l i s h e df or$ μ $o n t h e p a t h s p a ceo v er$ 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