Journal ArticleDOI
Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space
K. Suresh Kumar,Chandan Pal +1 more
Reads0
Chats0
TLDR
In this article, the authors prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.Abstract:
In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.read more
Citations
More filters
Journal ArticleDOI
Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions
Ari Arapostathis,Anup Biswas +1 more
TL;DR: In this article, the authors considered the infinite horizon risk-sensitive problem for nondegenerate diffusions with a compact action space, and controlled through the drift, and showed that there always exists a solution to the risk sensitive Hamilton-Jacobi-Bellman (HJB) equation.
Journal ArticleDOI
Risk-Sensitive Discounted Continuous-Time Markov Decision Processes with Unbounded Rates
Xianping Guo,Zhong-Wei Liao +1 more
TL;DR: This paper attempts to study the risk-sensitive discounted continuous-time Markov decision processes with unbounded transition and cost rates with an emphasis on bounded transition/cost rates.
Journal ArticleDOI
Risk-sensitive continuous-time Markov decision processes with unbounded rates and Borel spaces
Xianping Guo,Junyu Zhang +1 more
TL;DR: This paper considers the finite-horizon risk-sensitive optimality for continuous-time Markov decision processes, and focuses on the more general case that the transition rates are unbounded, cost/reward rates are allowed to be unbounded from below and from above.
Journal ArticleDOI
Zero-sum risk-sensitive stochastic games for continuous time Markov chains
TL;DR: In this paper, the authors studied infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space.
Journal ArticleDOI
Risk sensitive control of pure jump processes on a general state space
Chandan Pal,Somnath Pradhan +1 more
TL;DR: In this paper, a stochastic control problem for pure jump processes on a general state space with risk sensitive discounted and ergodic cost criteria was studied, and the authors proved the existence of the discounted cost criterion.
References
More filters
Journal ArticleDOI
Spectral theory and limit theorems for geometrically ergodic Markov processes
TL;DR: In this paper, it was shown that for all complex α in a neighborhood of the origin, the normalized mean of exp(αSt ) (and not the logarithm of the mean) converges to ˇ f exponentially fast, where f is a solution of the multiplicative Poisson equation.
Posted Content
Spectral Theory and Limit Theorems for Geometrically Ergodic Markov Processes
TL;DR: In this paper, the authors considered the problem of finding a well-behaved solution for the multiplicative Poisson equation in a Markov chain with respect to a real-valued functional.
Journal ArticleDOI
Existence of Optimal Strategies Based on Specified Information, for a Class of Stochastic Decision Problems
TL;DR: In this article, the existence of admissible strategies for minimizing a continuous stochastic process with moment conditions on x, growth conditions on c, and continuity of c in its third variable (the control) was studied.
Book
Ergodic Control of Diffusion Processes
TL;DR: In this paper, the existence and characterization of optimal controls for ergodic control of non-degenerate diffusion processes are described and some related problems and open issues are discussed.
Journal ArticleDOI
Large Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes
TL;DR: In this paper, a new family of nonlinear Lyapunov drift criteria was introduced to characterize distinct subclasses of geometrically ergodic Markov processes in terms of simple inequalities for the nonlinear generator.