Hitting-time Distributions for Markov Chains

报 告 人:Jim Fill  (The Johns Hopkins University)

报告题目:Hitting-time Distributions for Markov Chains




I will discuss several representations of hitting-time distributions for (finite-state, ergodic, time-reversible, continuous- time)  Markov chains and stochastic constructions corresponding to these representations. Examples of representations of distributions considered, each of which has a link to published work of Mark Brown, are those of

(i) the hitting time from state 0 of any given state for a birth- and- death chain on the nonnegative integers, as a convolution of exponential distributions;

(ii) the hitting time from stationarity of any given state, as a mixture of N-fold convolution powers of a certain distribution, with N geometrically distributed; and

(iii) the hitting time from stationarity of any given set of states, as a convolution of certain modified-exponential distributions that relate to the interlacing eigenvalue theorem for bordered symmetric matrices.

Intertwinings of Markov semigroups (I'll explain what these are) play a key role in the stochastic constructions.

This is joint work with my Ph.D. advisee Vince Lyzinski.