Rate estimation for weak convergence of diffusion processes (Q2726275)

There are many results about the limit behaviours of diffusion processes. It is large deviation theory when the time is small and ergodic theory when the time becomes large. In both cases it is interesting to know about the rate of convergence. If the diffusion process is considered as a measure on the path space, we have weak convergence theory for diffusion processes when perturbating coefficients. However, up to now, there was no result about the rate of weak convergence of diffusion processes when perturbating its coefficients except using large deviation which just perturbates the noise part. An upper bound in terms of probability density functions for the Kantorovich-Wasserstein (K-W) distance is found between two random vectors. Then a recent result is applied to obtain an upper bound for K-W distance between two time sequences imbedded in two diffusion processes. Finally, the continuity norm of diffusion processes is used to get the desired result.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].