hitting time

Let (Xn)n0 be a Markov ChainMathworldPlanetmath. Then the hitting timePlanetmathPlanetmath for a subset A of I (the indexing set) is the random variableMathworldPlanetmath:


(set inf=).

This can be thought of as the time before the chain is first in a state that is a member of A.

Wite hiA for the probability that, starting from iI the chain ever hits the set A:


When A is a closed classPlanetmathPlanetmath, hiA is the absorption probability.

Title hitting time
Canonical name HittingTime
Date of creation 2013-03-22 14:18:18
Last modified on 2013-03-22 14:18:18
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 8
Author PrimeFan (13766)
Entry type Definition
Classification msc 60J10
Related topic MarkovChain
Related topic MeanHittingTime
Defines absorption probability