On uniqueness of mild solutions for dissipative stochastic evolution equations

Details On uniqueness of mild solutions for dissipative stochastic evolution equations On uniqueness of mild solutions for dissipative stochastic evolution equations

2010-01-29

arxiv.org/abs/1001.5413v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

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.

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