Parameter and moment bounds for a nonlinear stochastic ecology model

摘要

A differential equation model of a marine ecosystem is formulated as a stochastic process. The ecosystem is modeled by considering the random exchange of a chemical nutrient between three components of the ecosystem. The Chapman-Kolmogorov equations and the moment or cumulant generating functions for the process are derived to examine analytically the behavior of the moments of the process. Through the use of differential inequalities, bounds on the exchange rate parameters are derived to reflect component extinction. Bounds on the moments of the process are also obtained.