带Lévy噪声的Lotka-Volterra竞争模型的参数估计

Parameter estimation for competitive Lotka-Volterra model with Lévy noise

基于最小二乘原理,考虑离散观测下Lévy噪声驱动的随机二种群Lotka-Volterra竞争系统的参数估计问题。讨论在噪声强度ε→0和样本量n→∞的情况下,参数估计量的渐近一致性,并得到了估计量的渐近分布。最后,给出竞争模型参数估计的数值模拟,结果与理论一致。

Based on the principle of least square and the technique of discretization,parameter estimation problem for stochastic two-species Lotka-Volterra competitive system driven by Lévy noise is studied.The least squares estimator is proved to be asymptotic consistent in the caseε→0 and n→∞,and the asymptotic distribution of the estimator is obtained.Finally,the numerical simulation for the estimators of the competitive model is given,and the results are in line with the theory.