The fractional stochastic heat equation on the circle: Time regularity and potential theory

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Abstract

We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S1. We obtain sharp results on the Hölder continuity in time of the paths of the solution u = {u (t, x)}t ∈ R+, x ∈ S1. We then establish upper and lower bounds on hitting probabilities of u, in terms of the Hausdorff measure and Newtonian capacity respectively. © 2008 Elsevier B.V.

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Nualart, E., & Viens, F. (2009). The fractional stochastic heat equation on the circle: Time regularity and potential theory. Stochastic Processes and Their Applications, 119(5), 1505–1540. https://doi.org/10.1016/j.spa.2008.07.009

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