随机时滞Lotka-Volterra模型数值解的收敛性

Convergence of the Euler Scheme for Stochastic Delay Lotka-Volterra Model

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.

In general,most of stochastic delay Lotka-Volterra models do not have explicit solutions,thus numerical approximation schemes are invaluable tools for exploring their properties. According to the Euler method,using martingale inequality and Ito formula,the numerical approximation for a class of stochastic delay Lotka-Volterra model was discussed.In the last section,a numerical example is given.