July  2006, 6(4): 895-910. doi: 10.3934/dcdsb.2006.6.895

Time regularity of the evolution solution to fractional stochastic heat equation

1. 

Department of Mathematics, Purdue University, 150 N. University St, West Lafayette, IN 47907-2067, United States, United States

Received  March 2005 Revised  September 2005 Published  April 2006

We study the time-regularity of the paths of solutions to stochastic partial differential equations (SPDE) driven by additive infinite-dimensional fractional Brownian noise. Sharp sufficient conditions for almost-sure Hölder continuity, and other, more irregular levels of uniform continuity, are given when the space parameter is fixed. Additionally, a result is included on time-continuity when the solution is understood as a spatially Hölder-continuous-function-valued stochastic process. Tools used for the study include the Brownian representation of fractional Brownian motion, and sharp Gaussian regularity results.
Citation: Yalçin Sarol, Frederi Viens. Time regularity of the evolution solution to fractional stochastic heat equation. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 895-910. doi: 10.3934/dcdsb.2006.6.895
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