Open Access
2013 On a class of martingale problems on Banach spaces
Markus Kunze
Author Affiliations +
Electron. J. Probab. 18: 1-30 (2013). DOI: 10.1214/EJP.v18-2924


We introduce the local martingale problem associated to semilinear stochastic evolution equations driven by a cylindrical Wiener process and establish a one-to-one correspondence between solutions of the martingale problem and (analytically) weak solutions of the stochastic equation. We also prove that the solutions of well-posed equations are strong Markov processes. We apply our results to semilinear stochastic equations with additive noise where the semilinear term is merely measurable and to stochastic reaction-diffusion equations with Hölder continuous multiplicative noise.


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Markus Kunze. "On a class of martingale problems on Banach spaces." Electron. J. Probab. 18 1 - 30, 2013.


Accepted: 11 December 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1367.60043
MathSciNet: MR3145051
Digital Object Identifier: 10.1214/EJP.v18-2924

Primary: 60H15
Secondary: 60J25

Keywords: local martingale problem , Stochastic partial differential equations , strong Markov property

Vol.18 • 2013
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