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Consider the general 2-state chain, where P₁,2 = a, P2,1 = b. Give necessary and sufficient conditions for the chain (i) to be aperiodic, (ii) to possess an absorbing state, (iii) to have at least one stationary distribution, (iv) to have exactly one stationary distribution.

Consider the general 2-state chain, where P₁,2 = a, P2,1 = b. Give necessary and sufficient conditions for the chain (i) to be aperiodic, (ii) to possess an absorbing state, (iii) to have at least one stationary distribution, (iv) to have exactly one stationary distribution.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the general 2-state chain, where P₁,2 = a, P2,1 = b. Give necessary and sufficient conditions for the chain (i) to be aperiodic, (ii) to possess an absorbing state, (iii) to have at least one stationary distribution, (iv) to have exactly one stationary distribution.
Transcribed Image Text:Consider the general 2-state chain, where P₁,2 = a, P2,1 = b. Give necessary and sufficient conditions for the chain (i) to be aperiodic, (ii) to possess an absorbing state, (iii) to have at least one stationary distribution, (iv) to have exactly one stationary distribution.
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