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.
| Original language | English |
|---|---|
| Article number | 57 |
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Electronic Journal of Probability |
| Volume | 18 |
| DOIs | |
| Publication status | Published - May 2013 |