Adaptive estimation for small diffusion processes based on sampled data

08/03/2021

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by   Tetsuya Kawai, et al.

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We consider parametric estimation for multi-dimensional diffusion processes with a small dispersion parameter ε from discrete observations. For parametric estimation of diffusion processes, the main targets are the drift parameter α and the diffusion parameter β. In this paper, we propose two types of adaptive estimators for (α,β) and show their asymptotic properties under ε→0, n→∞ and the balance condition that (ε n^ρ)^-1 =O(1) for some ρ≥ 1/2. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.