Geodesic
On the probabilistic multichain Poisson equation
Onésimo Hernández-Lerma1 ; Jean B. Lasserre2
1 Departamento de Matemáticas CINVESTAV-IPN A. Postal 14-740 México, D.F. 07000, México
2 LAAS-CNRS 7 Av. du Colonel Roche 31077 Toulouse Cedex 4, France
Applicationes Mathematicae, Tome 28 (2001) no. 2, pp. 225-243.

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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.
DOI : 10.4064/am28-2-8
Mots-clés : paper introduces necessary sufficient conditions existence solutions probabilistic multichain poisson equation hbox hskip hbox hskip hbox h ph given charge where markov kernel transition probability function general measurable space existence conditions derived via three different approaches using canonical pairs ces averages resolvents

Onésimo Hernández-Lerma 1 ; Jean B. Lasserre 2

1 Departamento de Matemáticas CINVESTAV-IPN A. Postal 14-740 México, D.F. 07000, México
2 LAAS-CNRS 7 Av. du Colonel Roche 31077 Toulouse Cedex 4, France 
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Onésimo Hernández-Lerma; Jean B. Lasserre. On the probabilistic
multichain Poisson equation. Applicationes Mathematicae, Tome 28 (2001) no. 2, pp. 225-243. doi : 10.4064/am28-2-8. http://geodesic.mathdoc.fr/articles/10.4064/am28-2-8/

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