Absolute Continuity of Symmetric Markov Processes

Gaussian processes and the local times of symmetric Lévy processes

We give a relatively simple proof of the necessary and sufficient condition for the joint continuity of the local times of symmetric Lévy processes. This result was obtained in 1988 by M. Barlow and J. Hawkes without requiring that the Lévy processes be symmetric. In 1992 the authors used a very different approach to obtain necessary and sufficient condition for the joint continuity of the loca...

Moduli of Continuity of Local Times of Strongly Symmetric Markov Processes via Gaussian Processes

1. Introduction. In this paper we show that the moduli of continuity of the local times

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Results on Sym \ 1 Etric Stable Distributions and Processes

This work investigates properties of symmetric stable distributions and stochastic processes. A necessary and sufficient condition is presented for a regression involving symmetric stable random variables to be linear. We introduce the notion of n-fold dependence for symmetric stable random variables and under this condition characterize all monomials in such random variables for which moments ...

On General Perturbations of Symmetric Markov Processes

Let X be a symmetric right process, and let Z = {Zt, t ≥ 0} be a multiplicative functional of X that is the product of a Girsanov transform, a Girsanov transform under time-reversal and a continuous Feynman-Kac transform. In this paper we derive necessary and sufficient conditions for the strong L-continuity of the semigroup {Tt, t ≥ 0} given by Ttf(x) = Ex [Ztf(Xt)], expressed in terms of the ...