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Applied Mathematics & Optimization

, Volume 68, Issue 3, pp 311–331 | Cite as

Risk-Sensitive Control of Pure Jump Process on Countable Space with Near Monotone Cost

  • K. Suresh KumarEmail author
  • Chandan Pal
Article

Abstract

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.

Keywords

Risk-sensitive control Controlled Markov chain Multiplicative dynamic programming principle Harnack’s inequality Near monotone cost 

Notes

Acknowledgement

The authors are thankful to the referee for giving several suggestions which improved the readability of the paper.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia

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