The Poisson Equation
Onésimo Herná-Lerma, Jean Bernard Lasserre · Birkhäuser Basel eBooks · 2003
In this chapter we are concerned with necessary and/or sufficient conditions for the existence of solutions (g , h) to the probabilistic multichain Poisson equation (a) g = Pg , and (b) g + h — Ph = f with a given function f , called a “charge”, where P is the t.p.f. of a MC on a general measurable space (X , 13). The existence conditions are derived via three different approaches, using canonical pairs, Cesàro averages, and resolvents, in §§8.3, 8.4 and 8.5, respectively. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.