Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises

Abstract EN

Stochastic Lotka–Volterra model driven by small α-stable noises is used to describe population dynamics perturbed by random environment.

However, parameters in the model are always unknown.

The contrast function is given to obtain least squares estimators.

The consistency and the rate of convergence of the least squares estimators are proved, and the asymptotic distribution of the estimators are derived by Markov inequality, Cauchy–Schwarz inequality, and Gronwall’s inequality.

Some numerical examples are provided to verify the effectiveness of the estimators.