Risk-Sensitive Control of Pure Jump Process on Countable Space with Near Monotone Cost
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In this article, we study risk-sensitive control problem with controlled continuous time pure jump process on a countable space as state dynamics. We prove multiplicative dynamic programming principle, elliptic and parabolic Harnack’s inequalities. Using the multiplicative dynamic programing principle and the Harnack’s inequalities, we prove the existence and a characterization of optimal risk-sensitive control under the near monotone condition.
KeywordsRisk-sensitive control Controlled Markov chain Multiplicative dynamic programming principle Harnack’s inequality Near monotone cost
The authors are thankful to the referee for giving several suggestions which improved the readability of the paper.
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