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Theory of Probability and Mathematical Statistics

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Persistence and extinction in a stochastic nonautonomous logistic model of population dynamics


Authors: O. D. Borysenko and D. O. Borysenko
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 67-75
MSC (2010): Primary 60H10; Secondary 60J75, 60G51, 92D25
DOI: https://doi.org/10.1090/tpms/1080
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: The nonautonomous logistic differential equation is studied for the case where the rate of the population growth coefficient is perturbed by a white noise or by a centered or noncentered Poisson noise. Sufficient conditions are obtained for the almost sure population extinction, nonpersistence of the population in the mean, weak persistence of the population in the mean, and strong persistence of the population in the mean.


References [Enhancements On Off] (What's this?)

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Additional Information

O. D. Borysenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: odb@univ.kiev.ua

D. O. Borysenko
Affiliation: Department of Integral and Differential Equations, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email: dima.borisenko.wrk@gmail.com

DOI: https://doi.org/10.1090/tpms/1080
Keywords: Nonautonomous logistic stochastic differential equation, centered and noncentered Poisson noise, extinction, nonpersistence in the mean, weak persistence in the mean, strong persistence in the mean
Received by editor(s): August 20, 2018
Published electronically: February 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society