Bernoulli

  • Bernoulli
  • Volume 5, Number 2 (1999), 275-298.

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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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.

Article information

Source
Bernoulli, Volume 5, Number 2 (1999), 275-298.

Dates
First available in Project Euclid: 5 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1173147907

Mathematical Reviews number (MathSciNet)
MR1681699

Zentralblatt MATH identifier
0932.60072

Keywords
Besov spaces Malliavin calculus parabolic SPDEs

Citation

Morien, Pierre-Luc. The Hölder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation. Bernoulli 5 (1999), no. 2, 275--298. https://projecteuclid.org/euclid.bj/1173147907


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References

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