Monotonicity and complete monotonicity for continuous-time Markov chains

Drift and monotonicity conditions for continuous-time controlled Markov chains with an average criterion

In this paper, we give conditions for the existence of average optimal policies for continuous-time controlled Markov chains with a denumerable state–space and Borel action sets. The transition rates are allowed to be unbounded, and the reward/cost rates may have neither upper nor lower bounds. In the spirit of the “drift and monotonicity” conditions for continuous-time Markov processes, we pro...

A Monotonicity in Reversible Markov Chains

In this paper we identify a monotonicity in all countable-state-space reversible Markov chains and examine several consequences of this structure. In particular, we show that the return times to every state in a reversible chain have a decreasing hazard rate on the subsequence of even times. This monotonicity is used to develop geometric convergence rate bounds for time-reversibleMarkov chains....

Monotonicity in Markov Reward and Decision Chains: Theory and Applications

This paper focuses on monotonicity results for dynamic systems that take values in the natural numbers or in more-dimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth. We concentrate on results that are obtained by inductively proving properties of the dynamic pro...

Continuous Time Markov Chains

Discrete-time Markov chains are useful in simulation, since updating algorithms are easier to construct in discrete steps. They can also be useful as crude models of physical, biological, and social processes. However, in the physical and biological worlds time runs continuously, and so discrete-time mathematical models are not always appropriate. This is especially true in population biology –...

Continuous-time Markov Chains