English

Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation

Probability 2015-01-28 v1

Abstract

Let u = {u(t, x), t \in [0, T ], x \in R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect to the time and space variable, respectively. In particular, we derive their exact uniform and local moduli of continuity and Chung-type laws of the iterated logarithm.

Keywords

Cite

@article{arxiv.1501.06828,
  title  = {Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation},
  author = {Ciprian A. Tudor and Yimin Xiao},
  journal= {arXiv preprint arXiv:1501.06828},
  year   = {2015}
}