Stochastic heat equation with random coefficients

We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the Skorohod integral deduced from Itô's formula for...

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Veröffentlicht in:	Probability theory and related fields 1999-08, Vol.115 (1), p.41-94
Hauptverfasser:	ALOS, E, LEON, J. A, NUALART, D
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematics Parabolic differential equations Partial differential equations Probability Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Stochastic analysis Thermodynamics White noise
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Beschreibung
Zusammenfassung:	We prove the existence of a unique solution for a one-dimensional stochastic parabolic partial differential equation with random and adapted coefficients perturbed by a two-parameter white noise. The proof is based on a maximal inequality for the Skorohod integral deduced from Itô's formula for this anticipating stochastic integral.
ISSN:	0178-8051 1432-2064
DOI:	10.1007/s004400050236