On the probabilistic multichain Poisson equation
Volume 28 / 2001
Applicationes Mathematicae 28 (2001), 225-243
MSC: 60J05, 60J45.
DOI: 10.4064/am28-2-8
Abstract
This paper introduces necessary and//or sufficient conditions for the existence of solutions $(g,h)$ to the probabilistic multichain Poisson equation $$\hbox {(a) }\ g=Pg\hskip 1em \hbox{and}\hskip 1em \hbox {(b) }\ g+h-Ph=f,$$ 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.
