This paper introduces necessary and/or sufficient conditions for the existence of solutions (g,h) to the probabilistic multichain Poisson equation (a) g = Pg and (b) g+h-Ph = f, with a given charge f, where P is a Markov kernel (or transition probability function) on a general measurable space. The existence conditions are derived via three different approaches, using (1) canonical pairs, (2) Cesàro averages, and (3) resolvents.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-8,
author = {On\'esimo Hern\'andez-Lerma and Jean B. Lasserre},
title = {On the probabilistic multichain Poisson equation},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {225-243},
zbl = {1006.60067},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-8}
}
Onésimo Hernández-Lerma; Jean B. Lasserre. On the probabilistic multichain Poisson equation. Applicationes Mathematicae, Tome 28 (2001) pp. 225-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-8/