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On a class of martingale problems on Banach spaces

   
@article{EJP2924,
	author = {Markus Kunze},
	title = {On a class of martingale problems on Banach spaces},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {18},
	year = {2013},
	keywords = {local Martingale problem, strong Markov property, stochastic partial differential equations},
	abstract = {
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.
},
	pages = {no. 104, 1-30},
	issn = {1083-6489},
	doi = {10.1214/EJP.v18-2924},    
        url = {http://ejp.ejpecp.org/article/view/2924}}