Work

Absolute continuity for SPDEs with irregular fundamental solution

Year: 2015

Type: article

Abstract: For a class of stochastic partial differential equations studied by Conus and Dalang, we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space. The proof relies on a method developed by Debussche and Romito.The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension $d\ge 1$, and also to the heat equation.This provides an extension of earlier results.

Source: Electronic Communications in Probability

DOI: 10.1214/ecp.v20-3831

Authors: Marta Sanz-Solé, André Süss

Institution: Universitat de Barcelona

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Ministerio de Economía y Competitividad, Dirección General de Investigación Científica y Técnica