Original scientific paper

https://doi.org/10.3336/gm.52.2.13

Local asymptotic mixed normality of approximate maximum likelihood estimator of drift parameters in diffusion model

Snježana Lubura Strunjak ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
Miljenko Huzak ; Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia

Abstract

We assume that the diffusion X satisfies a stochastic differential equation of the form: dXt=μ(Xt,θ)dt+σ0ν(Xt)dWt, with unknown drift parameter θ and known diffusion coefficient parameter σ0. We prove that approximate maximum likelihood estimator of drift parameter θ n obtained from discrete observations (XiΔn,0≤ i≤ n) along fixed time interval [0,T], and when Δn =T/n tends to zero, is locally asymptotic mixed normal, with covariance matrix which depends on MLE obtained from continuous observations (Xt,0≤ t≤ T) along fixed time interval [0,T], and on path (Xt,0≤ t≤ T).

Keywords

Asymptotic mixed normality; diffusion processes; discrete observation; parameter estimation

Hrčak ID:

189340

URI

https://hrcak.srce.hr/189340

Publication date:

13.11.2017.

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