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

Abstract.   We assume that the diffusion X satisfies a stochastic differential equation of the form: dX_t=μ(X_t,θ)dt+σ₀ν(X_t)dW_t, 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 (X_iΔn,0≤ i≤ n) along fixed time interval [0,T], and when Δ_n =T/n tends to zero, is locally asymptotic mixed normal, with covariance matrix which depends on MLE obtained from continuous observations (X_t,0≤ t≤ T) along fixed time interval [0,T], and on path (X_t,0≤ t≤ T).

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

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

DOI: 10.3336/gm.52.2.13

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