期刊
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
卷 97, 期 1, 页码 95-110出版社
ELSEVIER
DOI: 10.1016/S0304-4149(01)00126-0
关键词
Brownian motion; stochastic differential equation; explosion; boundedness; Ito's formula
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 (x)over dot(t) = f(x(t)) into the Ito 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. (C) 2002 Elsevier Science B.V. All rights reserved.
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