Stationary Markov Chains and Independent Random Variables

Central and Local Limit Theories in Markov Dependent Random Variables

Stationary Probabilities of Markov Chains

In this paper, based on probabilistic arguments, we obtain an explicit solution of the stationary distribution for a discrete time Markov chain with an upper Hessenberg time stationary transition probability matrix. Our solution then leads to a numerically stable and eecient algorithm for computing stationary probabilities. Two other expressions for the stationary distribution are also derived,...

Markov Chains , Coupling , Stationary Distribution

In this lecture, we will introduce Markov chains and show a potential algorithmic use of Markov chains for sampling from complex distributions. For a finite state space Ω, we say a sequence of random variables (Xt) on Ω is a Markov chain if the sequence is Markovian in the following sense, for all t, all x0, . . . , xt, y ∈ Ω, we require Pr(Xt+1 = y|X0 = x0, X1 = x1, . . . , Xt = xt) = Pr(Xt+1 ...

Random walks and Markov chains

This lecture discusses Markov chains, which capture and formalize the idea of a memoryless random walk on a finite number of states, and which have wide applicability as a statistical model of many phenomena. Markov chains are postulated to have a set of possible states, and to transition randomly from one state to a next state, where the probability of transitioning to a particular next state ...

Markov Chains and Random Walks

Let G = (V,E) be a connected, undirected graph with n vertices and m edges. For a vertex v ∈ V , Γ(v) denotes the set of neighbors of v in G. A random walk on G is the following process, which occurs in a sequence of discrete steps: starting at a vertex v0, we proceed at the first step to a random edge incident on v0 and walking along it to a vertex v1, and so on. ”Random chosen neighbor” will ...