Electronic Journal of Probability

On a class of martingale problems on Banach spaces

Markus Kunze

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J25: Continuous-time Markov processes on general state spaces

local Martingale problem strong Markov property stochastic partial differential equations

This work is licensed under a Creative Commons Attribution 3.0 License.


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

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