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.

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APA

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

MLA 8th

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 26 May. 2024.

MLA7

Aubrey, Ndovie . "Exponential convergence to a quasi-stationary distribution with applications to birth and death processes". Afribary, Afribary, 30 Mar. 2024. Web. 26 May. 2024. < https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes >.

Chicago

Aubrey, Ndovie . "Exponential convergence to a quasi-stationary distribution with applications to birth and death processes" Afribary (2024). Accessed May 26, 2024. https://afribary.com/works/exponential-convergence-to-a-quasi-stationary-distribution-with-applications-to-birth-and-death-processes

Document Details
Ndovie, Aubrey Field: Statistics Type: Paper 60 PAGES (10204 WORDS) (pdf)