2. Stationary Distributions Recall that a stationary distribution of a Markov chain is a probability distribution P(X) such that starting with it and applying the transition probabilities does not change it. That is, it satisfies P(X = x) = Σ P(X₁+1 = x | X₁ = x') P(X = x'). (a) Give an example of a Markov chain with two states and deterministic transitions where applying the mini forward algorithm does not necessarily converge to a stationary distribution (b) Show, nevertheless, that your example has a stationary distribution

2. Stationary Distributions Recall that a stationary distribution of a Markov chain is a probability distribution P(X) such that starting with it and applying the transition probabilities does not change it. That is, it satisfies P(X = x) = Σ P(X₁+1 = x | X₁ = x') P(X = x'). (a) Give an example of a Markov chain with two states and deterministic transitions where applying the mini forward algorithm does not necessarily converge to a stationary distribution (b) Show, nevertheless, that your example has a stationary distribution

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 9EQ

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