Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

David Nualart, Lluís Quer-Sardanyons

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d ≥ 1 and d ≤ 3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. © 2009 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)3914-3938
JournalStochastic Processes and their Applications
Volume119
DOIs
Publication statusPublished - 1 Nov 2009

Keywords

  • Gaussian bounds
  • Malliavin calculus
  • Spatially homogeneous Gaussian noise
  • Stochastic partial differential equations

Fingerprint Dive into the research topics of 'Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations'. Together they form a unique fingerprint.

Cite this