Some Polar Sets for the Generalized Brownian Sheet

摘要

The polar sets of stochastic processes have been studied by many authors. See for example, Ref. [1] first investigated the relationship between capacity and polar sets for the Brownian motion. These results have been extended partially to more generalprocesses with stationary and independent increments by Hawkesc ] and Kahane[3], to fractional Brownian motion by Testard[4'5] and Xiao[6], to Brownian sheet by Khoshnevisan[7], and recently to generalized Brownian sheet by Chen[8]. Taylor and Watson[9]also proved similar results for the polar sets for the heat equation. In this article, we are concerned with some interesting sets by the method of Khoshnevisan[7] which are avoided by the path of the generalized Brownian sheet. In the language of Markov processes, such sets are said to be polar.