We consider an Ornstein–Uhlenbeck process with values in R_n driven by a Levy process (Z_t) taking values in R_d with d possibly smaller than n. The Levy noise can have a degenerate or even vanishing Gaussian component. Under a controllability rank condition and a mild assumption on the Levy measure of (Z_t), we prove that the law of the Ornstein–Uhlenbeck process at any time t > 0 has a density on R_n.

Densities for Ornstein–Uhlenbeck processes with jumps

PRIOLA, Enrico;
2009-01-01

Abstract

We consider an Ornstein–Uhlenbeck process with values in R_n driven by a Levy process (Z_t) taking values in R_d with d possibly smaller than n. The Levy noise can have a degenerate or even vanishing Gaussian component. Under a controllability rank condition and a mild assumption on the Levy measure of (Z_t), we prove that the law of the Ornstein–Uhlenbeck process at any time t > 0 has a density on R_n.
2009
41
41
50
http://arxiv.org/pdf/0708.1084v2
http://blms.oxfordjournals.org/
Ornstein-Uhlenbeck process; existence of density; SDEs with jumps
E. Priola; J. Zabczyk
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/71662
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