Mathematical Sciences: Coupling and Gradient Estimates, Conditional Brownian Motion

点击翻译按钮获取中文摘要

The principal investigator will conduct research in two areas of probability theory: coupling and gradient estimates, conditional Brownian motion. One goal of the first area is to give a new probabilistic approach to partial differential theory. The principal investigator will use coupling arguments to compare two or more stochastic averages for processes with differing initial distributions. He will use tools from differential geometry. The second area involves answering question in potential theory using probabilistic arguments.