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Usual and stochastic tail orders between hitting times for two Markov chains
Author(s) -
De Santis Emilio,
Spizzichino Fabio
Publication year - 2016
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2177
Subject(s) - markov chain , state space , mathematics , hitting time , markov property , state (computer science) , order (exchange) , statistical physics , markov process , markov chain mixing time , combinatorics , markov model , algorithm , statistics , physics , economics , finance
We consider time‐homogeneous Markov chains with state space E k ≡{0,1,…, k } and initial distribution concentrated on the state 0. For pairs of such Markov chains, we study the Stochastic Tail Order and the stochastic order in the usual sense between the respective first passage times in the state k . On this purpose, we will develop a method based on a specific relation between two stochastic matrices on the state space E k . Our method provides comparisons that are simpler and more refined than those obtained by the analysis based on the spectral gaps. Copyright © 2016 John Wiley & Sons, Ltd.