Stochastic heat equation with random coefficients

Authors
Alos, E Leon, JA Nualart, D
Citation
E. Alos et al., Stochastic heat equation with random coefficients, PROB TH REL, 115(1), 1999, pp. 41-94
Citations number
11
Categorie Soggetti
Mathematics
Journal title
PROBABILITY THEORY AND RELATED FIELDS
ISSN journal
01788051 → ACNP
Volume
115
Issue
1
Year of publication
1999
Pages
41 - 94
Database
ISI
SICI code
0178-8051(199909)115:1<41:SHEWRC>2.0.ZU;2-G
Abstract
We prove the existence of a unique solution for a one-dimensional stochasti c parabolic partial differential equation with random and adapted coefficie nts perturbed by a two-parameter white noise. The proof is based on a maxim al inequality for the Skorohod integral deduced from Ito's formula for this anticipating stochastic integral. Mathematics Subject Classification (1991 ): 60H15, 60H07.