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On additive and multiplicative (controlled) Poisson equations. (English) Zbl 1104.93057

Figiel, Tadeuz (ed.) et al., Approximation and probability. Papers of the conference held on the occasion of the 70th anniversary of Prof. Zbigniew Ciesielski, Bȩdlewo, Poland, September 20–24, 2004. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 72, 57-70 (2006).
Summary: Assuming that a Markov process satisfies the minorization property, existence and properties of the solutions to the additive and multiplicative Poisson equations are studied using splitting techniques. The problem is then extended to the study of risk sensitive and risk neutral control problems and corresponding Bellman equations.
For the entire collection see [Zbl 1091.47002].

MSC:

93E20 Optimal stochastic control
60J05 Discrete-time Markov processes on general state spaces
93C55 Discrete-time control/observation systems
49L20 Dynamic programming in optimal control and differential games
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