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[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1.

[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < Pij < 1.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.7: Cooridinates And Change Of Basis
Problem 58E
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[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < pij < 1. a) Show that a Markov chain with transition matrix 1 0 0 [/ 0 P = 1/4 1/2 1/4 0 1 has more than one stationary distributions. b) find the matrix that P" converges to, as n→ ∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.
Transcribed Image Text:[6] In Theorem 3, we required that all elements of the transition matrix P be strictly positive, that is, 0 < pij < 1. a) Show that a Markov chain with transition matrix 1 0 0 [/ 0 P = 1/4 1/2 1/4 0 1 has more than one stationary distributions. b) find the matrix that P" converges to, as n→ ∞, and verify that it is not a matrix with identical rows, i.e. not in the form Theorem 3 predicts.
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