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Uniqueness in Law of the stochastic convolution process driven by Lévy noise


 
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1. Title Title of document Uniqueness in Law of the stochastic convolution process driven by Lévy noise
 
2. Creator Author's name, affiliation, country Zdzisław Brzeźniak; University of York; United Kingdom
 
2. Creator Author's name, affiliation, country Erika Hausenblas; Montanuniversity Leoben; Austria
 
2. Creator Author's name, affiliation, country Elżbieta Motyl; University of Łódź; Poland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Poisson random measure, stochastic convolution process, uniqueness in law, stochastic partial differential equations
 
3. Subject Subject classification Primary 60H15; Secondary 60G57.
 
4. Description Abstract

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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Austrian Scinece Foundations
 
7. Date (YYYY-MM-DD) 2013-05-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2807
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2807
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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