Sample paths of the solution to the fractional-colored stochastic heat equation

Ciprian A. Tudor, Yimin Xiao
2017 Stochastics and Dynamics  
Let u = {u(t, x), t ∈ [0, T ], x ∈ 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. 2010 AMS Classification Numbers: 60H55, 60H07, 91G70.
doi:10.1142/s0219493717500046 fatcat:bgksws3oova4zisckdo6cxtlom