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Environmental Brownian noise suppresses explosions in population dynamics

Xuerong Mao, Glenn Marion and Eric Renshaw

Stochastic Processes and their Applications, 2002, vol. 97, issue 1, 95-110

Abstract: Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system into the Itô form dx(t)=f(x(t)) dt+g(x(t)) dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not.

Keywords: Brownian; motion; Stochastic; differential; equation; Explosion; Boundedness; Ito's; formula (search for similar items in EconPapers)
Date: 2002
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