Analytic Form of the Quasi-stationary Distribution of a Simple Birth-Death Process
- Authors
- Lee, Julian
- Issue Date
- Sep-2020
- Publisher
- KOREAN PHYSICAL SOC
- Keywords
- Stochastic process; Quasi-stationary state; Master equation; Analytic solution; Population dynamics
- Citation
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY, v.77, no.6, pp.457 - 462
- Journal Title
- JOURNAL OF THE KOREAN PHYSICAL SOCIETY
- Volume
- 77
- Number
- 6
- Start Page
- 457
- End Page
- 462
- URI
- http://scholarworks.bwise.kr/ssu/handle/2018.sw.ssu/39694
- DOI
- 10.3938/jkps.77.457
- ISSN
- 0374-4884
- Abstract
- I consider a simple birth-death model with an absorbing state, where the stable fixed point of the corresponding deterministic mean-field dynamics turns into a transient peak of the probability distribution due to the presence of a tiny fluctuation. The model satisfies the detailed-balance condition, enabling one not only to obtain the analytic form of a quasi-stationary distribution, but also to obtain the analytic form of the escape time under the assumption of quasi-stationarity. I argue that the quasi-steady distribution with exponentially decaying normalization is an excellent approximation of the dynamics at late times, especially for small fluctuations. The analytic expressions for the quasi-stationary distribution and the escape time are expected to be more accurate, hence more useful, for systems with larger sizes.
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Collections - College of Natural Sciences > School of Systems and Biomedical Science > 1. Journal Articles
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