Parametric estimation for partially hidden diffusion processes sampled at discrete times

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Iacus, Stefano Maria²  Uchida, Masayuki¹  Yoshida, Nakahiro^3,4 

[1] Osaka Univ, Grad Sch Engn Sci, Osaka 5608531, Japan

[2] Univ Milan, Dept Econ Business & Stat, I-20122 Milan, Italy

[3] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan

[4] Japan Sci & Technol Agcy, Tokyo, Japan

关键词: Discrete observations;    Partially observed systems;    Diffusion processes;   

DOI  :  10.1016/j.spa.2008.08.004

来源: Elsevier

【 摘 要 】

For a one-dimensional diffusion process X = {X(t): 0 <= t <= T}, we suppose that X(t) is hidden if it is below some fixed and known threshold tau, but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is the estimation of a finite-dimensional parameter in both drift and diffusion coefficients under a partially hidden diffusion process obtained by a discrete sampling scheme. It is assumed that the sampling Occurs at regularly spaced time intervals of length h(n) such that nh(n) = T. The asymptotic is when h(n) -> 0, T -> infinity and nh(n)(2) -> 0 as n -> infinity. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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