Asymptotic behavior of a solution of the non-autonomous logistic stochastic differential equation
Authors:
O. D. Borysenko and D. O. Borysenko
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 101 (2020), 39-50
MSC (2020):
Primary 60H10; Secondary 60G51, 92D25
DOI:
https://doi.org/10.1090/tpms/1110
Published electronically:
January 5, 2021
Full-text PDF
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Additional Information
Abstract: The non-autonomous logistic differential equation with coefficients perturbed by a white noise, or by a centered Poisson noise, or by a non-centered Poisson noise is studied. The existence of a unique global non-negative solution is proved. Sufficient conditions for the almost sure extinction, almost sure non-persistence in the mean, and almost sure weak persistence of a population are obtained.
References
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References
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- K. Golpalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992. MR 1163190
- M. Liu and K. Wanga, Persistence and extinction in stochastic non-autonomous logistic systems, J. Math. Anal. Appl., 375 (2011), 443–457. MR 2735535
- J. Bao and Ch. Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl., 391 (2012), 363–375. MR 2903137
- S. Wang, L. Wang, and T. Wei, A note on a competitive Lotka–Volterra model with Lévy noise, Filomat 31 (2017), no. 12, 3741–3748. MR 3703869
- O. D. Borysenko and D. O. Borysenko, Non-autonomous stochastic logistic differential equation with non-centered Poisson measure, Bull. Taras Shevchenko Nat. Univ. Kyiv, Series: Physics & Mathematics (2017), no. 4, 9–14.
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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
Keywords:
Non-autonomous logistic stochastic differential equation,
centered and non-centered Poisson noises,
extinction,
non-persistence in the mean,
weak persistence
Received by editor(s):
August 29, 2019
Published electronically:
January 5, 2021
Article copyright:
© Copyright 2020
American Mathematical Society
