Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property

Details Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property

2010-09-14

arxiv.org/abs/1009.2650v2

Mathematics

Probability

33 pages; article was shortened, application to reaction-diffusion equation added

Scientific paper

We prove under minimal assumptions on the coefficients that existence and uniqueness of solutions to semilinear stochastic evolution equations on a general separable Banach space E yields that the solutions are strong Markov processes. We also establish existence and uniqueness (thus by the above also the strong Markov property) of solutions for stochastic reaction-diffusion equations with polynomially bounded nonlinearity and Hoelder continuous multiplicative noise.

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