Stats4Grads: Long Term Behaviour of Imprecise Markov Chains
30 January 2008 13:00 in CM105
Much is known about the long-term behaviour of discrete Markov chains for which the transition matrix is known precisely. In the case of finite aperiodic time-homogeneous birth-death processes with a single absorbing state, for example, it is well known that absorption is certain, but that there exists a distribution which is stationary under the condition of non-absorption; this is known as the quasi-stationary distribution.
Of course, in practice, there is no reason to assume that the transition matrix will be precisely known. In this talk we consider Markov Chains of the kind described above, for which some elements of the transition matrix are not known precisely, but are known to exist within known intervals. Specifically, we discuss with examples the long-term behaviour of such chains, both with and without the condition of non-absorption. We will also consider the effect of removing the condition of time-homogeneity.
See the Stats4Grads page for more details about this series.