Extended Generators of Markov Processes and Applications

Tomasz R. Bielecki () and Ewa Frankiewicz ()
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Tomasz R. Bielecki: Illinois Institute of Technology
Ewa Frankiewicz: Warsaw University of Technology

Chapter Chapter 3 in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, 2006, pp 35-54 from Springer

Abstract: Abstract An extended generator for a semigroup of linear contractions corresponding to a Markov process on a Banach space is introduced and its fundamental properties are examined. It is argued that the extended generator is a better tool to analyze the behavior of the semigroup in various time scales (discrete and continuous) than the “classical” generator of a semigroup. Probabilistic interpretation of extended generators in the context of Markov processes and corresponding martingale process is also provided. A controlled martingale problem is examined. Suitable version of Bellman’s optimality equations are introduced, and the corresponding verification theorem, which extends the classical optimality results for continuous time and discrete time controls, is established.

Keywords: Markov processes; infinitesimal operator; martingale problem; stochastic control (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-387-33815-6_3

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DOI: 10.1007/0-387-33815-2_3

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