Regularity and Strict Positivity of Densities for the Nonlinear Stochastic Heat Equations (Memoirs of the American Mathematical Society, 273) - Softcover

Chen, Le; Hu, Yaozhong; Nualart, David

Softcover

ISBN 10: 1470450003 ISBN 13: 9781470450007

Verlag: American Mathematical Society, 2021

Inhaltsangabe

"In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone condition for the diffusion coefficient, we establish the smooth joint density at multiple points. The tool we use is Malliavin calculus. The main ingredient is to prove that the solutions to a related stochastic partial differential equation have negative moments ofall orders. Because we cannot prove u(t, x) D for measure-valued initial data, we need a localized version of Malliavin calculus. Furthermore, we prove that the (joint) density is strictly positive in the interior of the support of the law, where we allow both measure-valued initial data and unbounded diffusion coefficient. The criteria introduced by Bally and Pardoux are no longer applicable for the parabolic Anderson model. We have extended their criteria to a localized version. Our general framework includes the parabolic Anderson model as a special case"--

Über diesen Titel

Über die Autorin bzw. den Autor

Le Chen, Emory University, Atlanta, GA.

Yaozhong Hu, University of Alberta at Edmonton, Canada.

David Nualart, University of Kansas, Lawrence, KS.

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2021
• Sprache: Englisch
• ISBN 10: 1470450003
• ISBN 13: 9781470450007
• Einband: Taschenbuch
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar