Risk-sensitive discounted cost criterion for Continuous-time Markov decision processes on a general state space
In this paper, we consider risk-sensitive discounted control problem for continuous-time jump Markov processes taking values in general state space. The transition rates of underlying continuous-time jump Markov processes and the cost rates are allowed to be unbounded. Under certain Lyapunov conditi...
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Zusammenfassung: | In this paper, we consider risk-sensitive discounted control problem for
continuous-time jump Markov processes taking values in general state space. The
transition rates of underlying continuous-time jump Markov processes and the
cost rates are allowed to be unbounded. Under certain Lyapunov condition, we
establish the existence and uniqueness of the solution to the
Hamilton-Jacobi-Bellman (HJB) equation. Also we prove the existence of optimal
risk-sensitive control in the class of Markov control. |
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DOI: | 10.48550/arxiv.2104.12366 |