The distribution of the “mixing time” or the “time to stationarity” in a discrete time irreducible Markov chain, starting in state i, can be defined as the number of trials to reach a state sampled from the stationary distribution of the Markov chain. Expressions for the probability generating function, and hence the probability distribution of the mixing time starting in state i are derived an...

A measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain is considered. The statistic η π i ij j m j m = = ∑ 1 , where {πj} is the stationary distribution and mij is the mean first passage time from state i to state j of the Markov chain, is shown to be independent of the state i that the chain starts in (so that ηi = η for all i), is minimal i...

In the last years, several authors studied a class of continuous-time semi-Markov processes obtained by time-changing Markov hitting times independent subordinators. Such are governed integro-differential convolution equations generalized fractional type. The aim this paper is to develop discrete-time counterpart such theory and show relationships differences with r...

Considering difference equations in discrete space instead of differential equations in Euclidean space, we investigate a probabilistic formula for the solution of the Dirichlet problem for biharmonic functions. This formula involves the expectation of a weighted sum of the pay-offs at the successive times at which the Markov chain is in the complement of the domain. To make the infinite sum co...

This paper focuses on relay node scheduling method which is based on an improved discrete Markov chain. It presents a single relay node’s existing state, analyzes its access behavior, and summarizes various linear system design, according to our present balanced equations and form state transition probability, nodes are scheduled in relay network, the improved discrete time Markov chain is used...

We investigate the problem of model checking Interval-valued Discrete-time Markov Chains (IDTMC). IDTMCs are discrete-time finite Markov Chains for which the exact transition probabilities are not known. Instead in IDTMCs, each transition is associated with an interval in which the actual transition probability must lie. We consider two semantic interpretations for the uncertainty in the transi...