Abstract: Let be a random string process taking values in , specified by the following stochastic partial differential equation [Funaki (1983)]:
Mueller and Tribe (2002) have proved necessary and sufficient conditions for the -valued process to hit points and to have double points. In this talk, we continue their research by determining the Hausdorff and packing dimensions of the level sets and the sets of double times of the random string process . We also consider the Hausdorff and packing dimensions of the range and graph of the string.
This talk is based on a joint work with Yimin Xiao.