391 research outputs found
Densities for Ornstein-Uhlenbeck processes with jumps
We consider an Ornstein-Uhlenbeck process with values in R^n driven by a
L\'evy process (Z_t) taking values in R^d with d possibly smaller than n. The
L\'evy noise can have a degenerate or even vanishing Gaussian component.
Under a controllability condition and an assumption on the L\'evy 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. Moreover, when the L\'evy process is of -stable
type, , we show that such density is a -function
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