Imprecise continuous-time 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.

Imprecise Markov chains with absorption

Consider a discrete time Markov chain X = {X(n), n = 0, 1, . . .} with finite state space S = {−1} ∪ C, where C = {0, . . . , s} is a single communicating class with all states aperiodic. Assuming −1 can be reached from C, absorption is certain, making the limiting distribution (1, 0, . . . , 0). Instead of considering the limiting distribution, then, we condition at non-absorption at each time...