Invariant, super and quasi-martingale functions of a Markov process
Probability
2017-09-07 v1
Abstract
We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures.
Keywords
Cite
@article{arxiv.1709.01864,
title = {Invariant, super and quasi-martingale functions of a Markov process},
author = {Iulian Cîmpean and Lucian Beznea},
journal= {arXiv preprint arXiv:1709.01864},
year = {2017}
}