Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 104, 30 pp.
On a class of martingale problems on Banach spaces
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.
Electron. J. Probab., Volume 18 (2013), paper no. 104, 30 pp.
Accepted: 11 December 2013
First available in Project Euclid: 4 June 2016
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Kunze, Markus. On a class of martingale problems on Banach spaces. Electron. J. Probab. 18 (2013), paper no. 104, 30 pp. doi:10.1214/EJP.v18-2924. https://projecteuclid.org/euclid.ejp/1465064329