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april 1999 The Hölder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation
Pierre-Luc Morien
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Bernoulli 5(2): 275-298 (april 1999).

Abstract

In this paper we prove that the density p t ,x (y) of the solution of a white-noise-driven parabolic stochastic partial differential equation (SPDE) satisfying a strong ellipticity condition is 1 2 Lipschitz continuous with respect to (w.r.t.) t and 1 -ε Lipschitz continuous w.r.t. x for all ε ]0,1[ . In addition, we show that it belongs to the Besov space B 1 ,, w.r.t. x . The proof is based on the Malliavin calculus of variations and on some refined estimates for the Green kernel associated with the SPDE.

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Pierre-Luc Morien. "The Hölder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation." Bernoulli 5 (2) 275 - 298, april 1999.

Information

Published: april 1999
First available in Project Euclid: 5 March 2007

zbMATH: 0932.60072
MathSciNet: MR1681699

Keywords: Besov spaces , Malliavin calculus , parabolic SPDEs

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability

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Vol.5 • No. 2 • april 1999
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