Continuous-time controlled Markov chains

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

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.

Simulation for Continuous-Time Markov Chains

This paper presents a simulation preorder for continuoustime Markov chains (CTMCs). The simulation preorder is a conservative extension of a weak variant of probabilistic simulation on fully probabilistic systems, i.e., discrete-time Markov chains. The main result of the paper is that the simulation preorder preserves safety and liveness properties expressed in continuous stochastic logic (CSL)...