The Quasistationary Behaviour Ofquasi - Birth - and - Death Processesn

Analytical and Computational Methods for Modelling the Long{term Behaviour of Evanescent Random Processes

There are a variety of stochastic systems arising in areas as diverse as wildlife management, chemical kinetics and reliability theory, which eventually \die out", yet appear to be stationary over any reasonable time scale. The notion of a quasistationary distribution has proved to be a potent tool in modelling this behaviour. In nite-state systems the existence of a quasistationary distributio...

Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains

We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix Q. We shall present conditions which ensure that any finite μ-invariant probability measure for Q is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes. QUASISTATIONA...

Quasistationary Distributions for Level-dependent Quasi-birth-and-death Processes

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its dete...

Spectral theory of metastability and extinction in birth-death systems.

We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type mA-->nA (m and n are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction stati...