Transportation Cost Inequality on Path Spaces with Uniform Distance

Fang, Shizan; Wang, Feng-Yu; Wu, Bo

Transportation Cost Inequality on Path Spaces with Uniform Distance

Authors

Fang, Shizan

Wang, Feng-Yu

Wu, Bo

Description

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 $M$ be a complete Riemnnian manifold and $μ$ the distribution of the diffusion process generated by $\ff 1 2\DD+Z$ where $Z$ is a $C^1$-vector field. When $\Ric-\nn Z$ is bounded below and $Z$ has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for $μ$ on the path space over $M$. A simple example is given to show the optimality of the condition.
to appear in Stochastic Processes and Applications