Parameter estimation for stochastic Lotka-Volterra model driven by small Lévy noises from discrete observations

Abstract

This paper is concerned with the problem of parameter estimation for stochastic Lotka-Volterra model driven by small Lévy noises from discrete observations. The least squares method is used to obtain the parameter estimators and the explicit formula of the estimation error is given. The consistency of the estimators are derived when a small dispersion coefficient $\epsilon \to 0$ and $n\to \infty$ simultaneously by using Cauchy-Schwarz inequality, Gronwall’s inequality, Markov inequality and dominated convergence. The asymptotic distribution of the estimation error is shown as well. Moreover, the simulation is made to verify the effectiveness of the least squares estimators.

Keywords:

• Stochastic Lotka-Volterra model
• Lévy noises
• discrete observations
• consistency
• asymptotic distribution