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On uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs

   
@article{EJP2049,
	author = {Richard Bass and Edwin Perkins},
	title = {On uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {stochastic partial differential equations; stochastic differential equ ations; uniqueness; perturbation; Jaffard's theorem},
	abstract = {
We give a sufficient conditions for uniqueness inlaw for the stochastic partial differential equation$$\frac{\partial u}{\partial t}(x,t)=\tfrac12 \frac{\partial^2 u}{\partial x^2}(x,t)+A(u(\cdot,t)) \dot W_{x,t},$$where $A$ is an operator mapping $C[0,1]$ into itself and $\dot W$ isa space-time white noise. The approach is to first prove uniquenessfor the martingale problem for the operator$$\mathcal{L} f(x)=\sum_{i,j=1}^\infty a_{ij}(x) \frac{\partial^2 f}{\partial x^2}(x)-\sum_{i=1}^\infty \lambda_i x_i \frac{\partial f}{\partial x_i}(x),$$where $\lambda_i=ci^2$ and the $a_{ij}$ is a positive definite boundedoperator in Toeplitz form.
},
	pages = {no. 36, 1-54},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-2049},    
        url = {http://ejp.ejpecp.org/article/view/2049}}