Stochastic heat equation with white-noise drift

Citation
E. Alos et al., Stochastic heat equation with white-noise drift, ANN IHP-PR, 36(2), 2000, pp. 181-218
Citations number
17
Categorie Soggetti
Mathematics
Journal title
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN journal
02460203 → ACNP
Volume
36
Issue
2
Year of publication
2000
Pages
181 - 218
Database
ISI
SICI code
0246-0203(200003/04)36:2<181:SHEWWD>2.0.ZU;2-5
Abstract
We study the existence and uniqueness of the solution for a one-dimensional anticipative stochastic evolution equation driven by a two-parameter Wiene r process W-t,W-x and based on a stochastic semigroup p (s, t, y, x). The k ernel p(s, t, y, x) is supposed to be measurable with respect to the increm ents of the Wiener process on [s, t] x R. The results are based on L-p-esti mates for the Skorohod integral. As a application we deduce the existence o f a weak solution for the stochastic partial differential equation partial derivative u/partial derivative t = partial derivative(2)u/partial derivative x(2) + (v) over dot(t, x) partial derivative u/partial derivativ e x + F(t, x, u) partial derivative(2)W/partial derivative t partial deriva tive x, where (v) over dot(t, x) is a white-noise in time. (C) 2000 Editions scient ifiques et medicales Elsevier SAS.