Markoff Chains with Reverse Transitions

A Generalization of Poisson's Distribution for Markoff Chains.

Entropy Rate for Hidden Markov Chains with rare transitions

We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero. Let (Xn) be a Markov chain with finite state space S and transition matrix P (p) and let (Yn) be the Hidden Markov chain observed by passing (Xn...

Statistics of transitions for Markov chains with periodic forcing

The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular a functional Central Limit Theorem can be proven for the number of transitions between two states chosen in the whole finite state space of the Mark...

Compositionality for Markov Reward Chains with Fast Transitions

A parallel composition is defined for Markov reward chains with fast transitions and for discontinuous Markov reward chains. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are τ -lumping and τ -reduction. Discontinuous Markov reward chains are ‘limits’ of Markov reward chains with ...

Markov Chains with Rare Transitions and Simulated Annealing