IJPAM: Volume 68, No. 4 (2011)

ABSOLUTE CONTINUITY OF A LAW OF AN ITÔ
PROCESS DRIVEN BY A LÉVY PROCESS
TO ANOTHER ITÔ PROCESS
Erika Hausenblas
Department of Mathematics and Information-Technology
Montana University of Leoben
Franz Josefstraße 18, Leoben, 8700, AUSTRIA
e-mail: [email protected]


Abstract. Let $\xi_1$ and $\xi_2$ be two solutions of two stochastic differential equations with respect to Lévy noise taking values in a certain type of Banach space. Let $\CQ_1$ and $\CQ_2$ be the probability measures on the corresponding Skorohod space induced by $\xi_1$ and $\xi_2$, respectively. In the paper we are interested under which conditions $\CQ_1$ is absolute continuous with respect to $\CQ_2$. Moreover, we give an explicit formula for the Radon Nikodym derivative of $\CQ_1$ with respect to $\CQ_2$.

Received: January 28, 2011

AMS Subject Classification: 60H07, 60H10, 60J75, 62A99

Key Words and Phrases: Itô processes, Poisson random measures, absolutely continuity, Lévy processes

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 4