Densities for Ornstein-Uhlenbeck processes with jumps

Details Densities for Ornstein-Uhlenbeck processes with jumps Densities for Ornstein-Uhlenbeck processes with jumps

2007-08-08

arxiv.org/abs/0708.1084v2

Mathematics

Probability

Scientific paper

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 $\alpha$-stable type, $\alpha \in (0,2)$, we show that such density is a $C^{\infty}$-function.

Affiliated with

Also associated with

No associations

Rating

Densities for Ornstein-Uhlenbeck processes with jumps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Densities for Ornstein-Uhlenbeck processes with jumps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Densities for Ornstein-Uhlenbeck processes with jumps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215652