Hitting Time Distribution for Skip-Free Markov Chains: A Simple Proof
Probability
2013-01-31 v1
Abstract
A well-known theorem for an irreducible skip-free chain with absorbing state , under some conditions, is that the hitting (absorbing) time of state starting from state 0 is distributed as the sum of independent geometric (or exponential) random variables. The purpose of this paper is to present a direct and simple proof of the theorem in the cases of both discrete and continuous time skip-free Markov chains. Our proof is to calculate directly the generation functions (or Laplace transforms) of hitting times in terms of the iteration method.
Keywords
Cite
@article{arxiv.1301.7180,
title = {Hitting Time Distribution for Skip-Free Markov Chains: A Simple Proof},
author = {Wenming Hong and Ke Zhou},
journal= {arXiv preprint arXiv:1301.7180},
year = {2013}
}