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2013 Uniqueness in Law of the stochastic convolution process driven by Lévy noise
Zdzisław Brzeźniak, Erika Hausenblas, Elżbieta Motyl
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Electron. J. Probab. 18: 1-15 (2013). DOI: 10.1214/EJP.v18-2807


We will give a proof of the following fact. If $\mathfrak{A}_1$ and $\mathfrak{A}_2$, $\tilde \eta_1$ and $\tilde \eta_2$, $\xi_1$ and $\xi_2$ are two examples of filtered probability spaces, time homogeneous compensated Poisson random measures, and progressively measurable Banach space valued processes such that the laws on $L^p([0,T],{L}^{p}(Z,\nu ;E))\times \mathcal{M}_I([0,T]\times Z)$ of the pairs $(\xi_1,\eta_1)$ and $(\xi_2,\eta_2)$, are equal, and $u_1$ and $u_2$ are the corresponding stochastic convolution processes, then the laws on $ (\mathbb{D}([0,T];X)\cap L^p([0,T];B)) \times L^p([0,T],{L}^{p}(Z,\nu ;E))\times \mathcal{M}_I([0,T]\times Z) $, where $B \subset E \subset X$, of the triples $(u_i,\xi_i,\eta_i)$, $i=1,2$, are equal as well. By $\mathbb{D}([0,T];X)$ we denote the Skorokhod space of $X$-valued processes.


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Zdzisław Brzeźniak. Erika Hausenblas. Elżbieta Motyl. "Uniqueness in Law of the stochastic convolution process driven by Lévy noise." Electron. J. Probab. 18 1 - 15, 2013.


Accepted: 21 May 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1284.60125
MathSciNet: MR3065867
Digital Object Identifier: 10.1214/EJP.v18-2807

Primary: 60H15
Secondary: 60G57

Keywords: Poisson random measure , stochastic convolution process , Stochastic partial differential equations , uniqueness in law

Vol.18 • 2013
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