We combine earlier investigations of linear systems with Lévy fluc-We give a complete construction of the Ornstein-Uhlenbeck-Cauchy process as a fully computable model of an anomalous transport and a paradigm example of Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the nonexistence of all moments, we determine local characteristics (forward drift) of the process, generators ...

In this paper the connection between the dipole moment tensorD and the spin four-tensor S is formulated in the form of the generalized Uhlenbeck-Goudsmit hypothesis, D = gSS . It is also found that the spin four-tensor S can be decomposed into two 4-vectors, the usual “space-space” intrinsic angular momentum S and a new one, the “time-space” intrinsic angular momentum Z, which are both equally ...

This paper uses linear programming to numerically evaluate the Laplace transform of the exit time distribution and the resolvent of the moments of various Markov processes in bounded regions. The linear programming formulation is developed from a martingale characterization of the processes and the use of occupation measures. The LP approach naturally provides both upper and lower bounds on the...

A generalized Mehler semigroup (Ornstein-Uhlenbeck semigroup) associated with some strongly continuous semigroup of linear operators on a real separable Hilbert space may be defined by using a skew convolution semigroup. Under a mild moment assumption, it is proved that the characteristic functional of any centered skew convolution semigroup is absolutely continuous and characterizations are gi...

Abstract: We consider an Ornstein-Uhlenbeck process with values in Rn driven by a Lévy process (Zt) taking values in R d with d possibly smaller than n. The Lévy noise can have a degenerate or even vanishing Gaussian component. Under a controllability condition and an assumption on the Lévy measure of (Zt), we prove that the law of the Ornstein-Uhlenbeck process at any time t > 0 has a density ...

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random variables, which are independent and identically dis...

In this article we establish a large deviation principle for the family {ν ε : ε ∈ (0, 1)} of distributions of the scaled stochastic processes {P − log √ ε Z t } t≤1 , where (Z t) t∈[0,1] is a square-integrable martingale over Brownian filtration and (P t) t≥0 is the Ornstein-Uhlenbeck semigroup. The rate function is identified as well in terms of the Wiener-Itô chaos decomposition of the termi...