Glasnik Matematicki, Vol. 52, No. 2 (2017), 377-410.

LOCAL ASYMPTOTIC MIXED NORMALITY OF APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR OF DRIFT PARAMETERS IN DIFFUSION MODEL

Snježana Lubura Strunjak and Miljenko Huzak

Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia
e-mail: snjezana.lubura.strunjak@math.hr
e-mail: miljenko.huzak@math.hr

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 (Xn,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).

2010 Mathematics Subject Classification.   62M05, 62F12, 60J60.

Key words and phrases.   Asymptotic mixed normality, diffusion processes, discrete observation, parameter estimation.


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DOI: 10.3336/gm.52.2.13


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