Markov processes on an entrance boundary

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 Effect of Boundary Constraints on Markov-Modulated Diffusion Processes

ON THE GENERALIZATION OF N-PLE MARKOV PROCESSES

The notion of N-ple Markov process is defined in a quite general framework and it is shown that N-ple Markov processes-arel inear combinationso f some martingales

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.

Boundary Harnack Inequality for Markov Processes with Jumps

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds for positive harmonic functions in arbitrary open sets. It applies, e.g., to many subordinate Brownian motions, Lévy processes with and without continuous p...