Parameter estimation for a class of stochastic differential equations driven by small stable noises from discrete observations

Abstract

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points t i = i/n, i = 1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator (LSE) when a small dispersion parameter ɛ → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.