### Talk by Manuel Lladser (University of Colorado, Boulder)

Date and Time: Thursday, December 5, 10:00 AM in AP&M 6402

Title: Breaking the memory of a Markov chain

Abstract:
In a report published in 1937, Doeblin - who is regarded the father of
the "coupling method" - introduced an ergodicity coefficient that
provided the first necessary and sufficient condition for the weak
ergodicity of non-homogeneous Markov chains over finite state spaces.

In today's jargon, Doeblin's coefficient corresponds to the maximal
coupling of the probability transition kernels associated with a Markov
chain, and the Monte Carlo literature has (often implicitly) used it to
draw perfectly from the stationary distribution of a homogeneous Markov
chain over a Polish state space.

In this talk, I will show how Doeblin's coefficient can be used to
approximate the distribution of additive functionals of homogeneous
Markov chains, particularly sojourn-times, instead of characterizing
asymptotic objects such as stationary distributions. The methodology
leads to easy to compute and explicit error bounds in total variation
distance, and gives access to approximations in Markov chains that are
too long for exact calculation but also too short to rely on Normal
approximations or stationary assumptions underlying Poisson
approximations.