For a one-dimensional diffusion process View the MathML source, we suppose that X(t) is hidden if it is below some fixed and known threshold τ, 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 hn such that nhn=T. The asymptotic is when hn→0, T→∞ and View the MathML source as n→∞. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved
Parametric estimation for partially hidden diffusion processes sampled at discrete times / S.M. Iacus, M. Uchida, N. Yoshida. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 119:5(2009), pp. 1580-1600.
Parametric estimation for partially hidden diffusion processes sampled at discrete times
S.M. IacusPrimo
;
2009
Abstract
For a one-dimensional diffusion process View the MathML source, we suppose that X(t) is hidden if it is below some fixed and known threshold τ, 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 hn such that nhn=T. The asymptotic is when hn→0, T→∞ and View the MathML source as n→∞. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are provedFile | Dimensione | Formato | |
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