Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs

Richard F. Bass; Edwin A. Perkins

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arXiv · 1102.5257

Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs

Richard F. Bass·Edwin A. Perkins

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Abstract

We prove uniqueness in law for a class of parabolic stochastic partial differential equations in an interval driven by a functional A(u) of the temperature u times a space-time white noise. The functional A(u) is H\"older continuous in u of order greater than 1/2. Our method involves looking at an associated system of infinite-dimensional stochastic differential equations and we obtain a uniqueness result for such systems.

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Richard F. Bass, Edwin A. Perkins. 2011-02-25. Uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs. https://arxiv.org/abs/1102.5257

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