SPD

Abstract

SPDEs is a relatively new subject in probability theory. It originated from filtering theory of random processes and the theory of random processes and the theory of measure-valued processes, which are also called superdiffusions. We present various relations of the theory of SPDEs to other areas of probability theory and the theory of partial differential equations. In particular, the law of square root for the Wiener process and the regularity of boundary points for random domains will be discussed. A quick introduction to Brownian motion and stochastic partial differential equations will be given.