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.
Aubrey, N (2024). Exponential convergence to a quasi-stationary distribution with applications to birth and death processes. Afribary. Retrieved from https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes
Aubrey, Ndovie "Exponential convergence to a quasi-stationary distribution with applications to birth and death processes" Afribary. Afribary, 30 Mar. 2024, https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes. Accessed 22 Nov. 2024.
Aubrey, Ndovie . "Exponential convergence to a quasi-stationary distribution with applications to birth and death processes". Afribary, Afribary, 30 Mar. 2024. Web. 22 Nov. 2024. < https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes >.
Aubrey, Ndovie . "Exponential convergence to a quasi-stationary distribution with applications to birth and death processes" Afribary (2024). Accessed November 22, 2024. https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes