1Departamento de Matemáticas CINVESTAV-IPN A. Postal 14-740 México, D.F. 07000, México 2LAAS-CNRS 7 Av. du Colonel Roche 31077 Toulouse Cedex 4, France
Applicationes Mathematicae, Tome 28 (2001) no. 2, pp. 225-243
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.
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
Affiliations des auteurs :
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
@article{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},
pages = {225--243},
year = {2001},
volume = {28},
number = {2},
doi = {10.4064/am28-2-8},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am28-2-8/}
}
TY - JOUR
AU - Onésimo Hernández-Lerma
AU - Jean B. Lasserre
TI - On the probabilistic
multichain Poisson equation
JO - Applicationes Mathematicae
PY - 2001
SP - 225
EP - 243
VL - 28
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multichain Poisson equation
%J Applicationes Mathematicae
%D 2001
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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
