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.
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