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Quasi stationary behaviour of markov chains

Objective



Stationary distributions describe the limiting behaviour of ergodic Markov chains, and as such they are valuable for studying real-world phenomena. On the other hand, some transient Markov chains also seem to reach a kind of equilibrium long before their real equilibrium sets in. This phenomenon is called quasi stationary behaviour. We can gain an understanding of this quasi stationary behaviour by studying a type of limiting conditional distribution. This distribution has already been described for Markov chains with an absorbing state but little attention has been given to Markov chains with a reflecting boundary.
Our goal is to determine necessary and sufficient conditions for the existence of this type of limiting conditional distributions for general Markov chains on an irreducible state space. As a first step, we plan to study branching processes with immigration, models for the backlog of a slotted ALOHA protocol, and branching processes with immigration and emigration/catastrophes.

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

UNIVERSITY OF DURHAM
Address
Science Laboratories, South Road
DH1 3LE Durham
United Kingdom

Participants (1)

Not available
Netherlands