Markov operators and OS-positive processes

Potential Operators for Markov Processes

Yosida's definition of potential operators for semigroups [17] makes it possible to deal with transient Markov processes and a class of recurrent Markov processes in a unified operator theoretical way. In this paper, we prove some general properties of his potential operators, show which Markov processes admit the potential operators, and investigate the cases of processes with stationary indep...

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

The KTH Visit in Semi-Markov Processes

Optimal prediction for positive self-similar Markov processes

This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in [9] under the assumption that X is a positive transient diffusion. We extend their result to the class of positive self-similar Markov processes by establishing a...

Some Explicit Identities Associated with Positive Self-similar Markov Processes

We consider some special classes of Lévy processes with no gaussian component whose Lévy measure is of the type π(dx) = e γx ν(e x − 1) dx, where ν is the density of the stable Lévy measure and γ is a positive parameter which depends on its characteristics. These processes were introduced in [10] as the underlying Lévy processes in the Lamperti representation of conditioned stable Lévy processe...