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ON UNIQUENESS OF MILD SOLUTIONS FOR DISSIPATIVE STOCHASTIC EVOLUTION EQUATIONS

CARLO MARINELLI

Facoltà di Economia, Università di Bolzano, Piazza Università 1, I-39100 Bolzano, Italy

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and

MICHAEL RÖCKNER

Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, D-33501 Bielefeld, Germany

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https://doi.org/10.1142/S0219025710004152Cited by:19 (Source: Crossref)

Abstract

In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried out in a formal way, without really justifying why and how one can do that. We provide sufficient conditions for uniqueness of mild solutions to a broad class of semilinear stochastic evolution equations with coefficients satisfying a monotonicity assumption.

Keywords:

AMSC: 60H15, 60G57

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