Time regularity of the evolution solution to fractional stochastic heat equation | Zendy

Yalçin Sarol | Zendy; Frédéri Viens | Zendy

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Time regularity of the evolution solution to fractional stochastic heat equation

Author(s) -

Yalçin Sarol,

Frédéri Viens

Publication year - 2006

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2006.6.895

Subject(s) - mathematics , fractional brownian motion , brownian motion , heat equation , hölder condition , stochastic differential equation , representation (politics) , brownian noise , function (biology) , mathematical analysis , brownian excursion , geometric brownian motion , diffusion process , computer science , statistics , white noise , evolutionary biology , politics , political science , law , biology , knowledge management , innovation diffusion

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 Holder 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 Holder-continuous-function-valued stochastic process. Tools used for the study include the Brownian representation of fractional Brownian motion, and sharp Gaussian regularity results.

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