Extended Poisson equation for weakly ergodic Markov processes
Extended Poisson equation for weakly ergodic Markov processes
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 …