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• W2022667068 abstract "A birth–death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λ n and a particle dies with instantaneous rate μ n . Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth–death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics." @default.
• W2022667068 created "2016-06-24" @default.
• W2022667068 creator A5039905606 @default.
• W2022667068 creator A5080170176 @default.
• W2022667068 date "2011-10-09" @default.
• W2022667068 modified "2023-09-30" @default.
• W2022667068 title "Transition probabilities for general birth–death processes with applications in ecology, genetics, and evolution" @default.
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• W2022667068 doi "https://doi.org/10.1007/s00285-011-0471-z" @default.
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