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2012 On uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs
Richard Bass, Edwin Perkins
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Electron. J. Probab. 17(none): 1-54 (2012). DOI: 10.1214/EJP.v17-2049

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.

Citation

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Richard Bass. Edwin Perkins. "On uniqueness in law for parabolic SPDEs and infinite-dimensional SDEs." Electron. J. Probab. 17 1 - 54, 2012. https://doi.org/10.1214/EJP.v17-2049

Information

Accepted: 26 May 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1244.60061
MathSciNet: MR2928719
Digital Object Identifier: 10.1214/EJP.v17-2049

Subjects:
Primary: 60H15
Secondary: 60H10

JOURNAL ARTICLE
54 PAGES


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