$\lambda $-continuous 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

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.

Continuous-time homogeneous Markov chains

On Markov Chains with Continuous State Space

In this expository paper, we p r o ve the following theorem, which m a y be of some use in studying Markov chain Monte Carlo methods like hit and run, the Metropolis algorithm, or the Gibbs sampler. Suppose a discrete-time Markov c hain is aperiodic, irreducible, and there is a stationary probability distribution. Then from almost all starting points the distribution of the chain at time n conv...