On continuous-time Markov chains with rewards. I.

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

Optimal Control of Ergodic Continuous-Time Markov Chains with Average Sample-Path Rewards

In this paper we study continuous-time Markov decision processes with the average sample-path reward (ASPR) criterion and possibly unbounded transition and reward rates. We propose conditions on the system’s primitive data for the existence of -ASPR-optimal (deterministic) stationary policies in a class of randomized Markov policies satisfying some additional continuity assumptions. The proof o...

Continuous-time homogeneous Markov chains

Verifying Continuous Time Markov Chains

We present a logical formalism for expressing properties of continuous time Markov chains. The semantics for such properties arise as a natural extension of previous work on discrete time Markov chains to continuous time. The major result is that the veriication problem is decidable; this is shown using results in algebraic and transcendental number theory.