Asymptotic behaviour of the stochastic Lotka-Volterra model |
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Authors: | Xuerong Mao Sotirios Sabanis Eric Renshaw |
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Affiliation: | Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK |
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Abstract: | This paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process, namely the Lotka-Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations. |
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Keywords: | Lotka-Volterra model Brownian motion Stochastic differential equation Moment boundedness Asymptotic behaviour |
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