Exponential convergence to a quasi-stationary distribution with applications to birth and death processes

Abstract:

In this project we study the exponential convergence of Markov processes to

quasi-stationary distributions (QSDs) with applications. Quasi-stationary

distributions are useful when it comes to understanding the behavior of

stochastic processes which appear to be persistent over a long time period

before reaching extinction. A review of the concept of stationarity and ergodicity is given. Next quasi-stationarity is defined. A simple example that

illustrates quasi-stationarity is considered- specifically the example of the finite state case. Finally, we choose a Corona Virus model, convert it to a

birth and death process, then show that it converges to a particular QSD

exponentially, we also choose the compartment of infected persons from the

model and show that it is a branching process that also converges to a QSD

over time.