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https://doi.org/10.3336/gm.59.1.10

An approximate maximum likelihood estimator of drift parameters in a multidimensional diffusion model

Miljenko Huzak ; Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
Snježana Lubura Strunjak ; Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
Andreja Vlahek vStrok ; Faculty of Chemical Engineering and Technology, University of Zagreb, 10 000 Zagreb, Croatia


Puni tekst: engleski pdf 596 Kb

str. 213-258

preuzimanja: 130

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Sažetak

For a fixed T and k2, a k-dimensional vector stochastic differential equation dXt=μ(Xt,θ)dt+ν(Xt)dWt, is studied over a time interval [0,T]. Vector of drift parameters θ is unknown. The dependence in θ is in general nonlinear. We prove that the difference between approximate maximum likelihood estimator of the drift parameter θnθn,T obtained from discrete observations (XiΔn,0in) and maximum likelihood estimator θ^θ^T obtained from continuous observations (Xt,0tT), when Δn=T/n tends to zero, converges stably in law to the mixed normal random vector with covariance matrix that depends on θ^ and on path (Xt,0tT). The uniform ellipticity of diffusion matrix S(x)=ν(x)ν(x)T emerges as the main assumption on the diffusion coefficient function.

Ključne riječi

Multidimensional diffusion processes, maximum likelihood estimation, uniform ellipticity, asymptotic mixed normality

Hrčak ID:

318148

URI

https://hrcak.srce.hr/318148

Datum izdavanja:

5.1.2025.

Posjeta: 347 *





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