On the probabilistic multichain Poisson equation

Volume 28 / 2001

Onésimo Hernández-Lerma, Jean B. Lasserre Applicationes Mathematicae 28 (2001), 225-243 MSC: 60J05, 60J45. DOI: 10.4064/am28-2-8


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.


  • Onésimo Hernández-LermaDepartamento de Matemáticas
    A. Postal 14-740
    México, D.F. 07000, México
  • Jean B. LasserreLAAS-CNRS
    7 Av. du Colonel Roche
    31077 Toulouse Cedex 4, France

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