Extended Poisson equation for weakly ergodic Markov processes

Veretennikov, A.; Kulik, A.

doi:10.1090/S0094-9000-2013-00871-0

Extended Poisson equation for weakly ergodic Markov processes

Authors: A. Yu. Veretennikov and A. M. Kulik
Translated by: N. Semenov
Journal: Theor. Probability and Math. Statist. 85 (2012), 23-39
MSC (2010): Primary 60H10, 60J10
DOI: https://doi.org/10.1090/S0094-9000-2013-00871-0
Published electronically: January 11, 2013
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Abstract: Solvability conditions for a Poisson equation with an extended generator of a general Markov process are obtained. The predictable part in the Doob–Meyer decomposition is described for a process of the form $g(X(t), Y(t))$, where $Y$ is a solution of a stochastic equation with the coefficients depending on $X$ and where the function $g=g(x,y)$ is defined as a family of solutions of the Poisson equation.

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