Parametric estimation for partially hidden diffusion processes sampled at discrete times

Details Parametric estimation for partially hidden diffusion processes sampled at discrete times Parametric estimation for partially hidden diffusion processes sampled at discrete times

2006-11-25

arxiv.org/abs/math/0611781v2

Mathematics

Statistics Theory

Scientific paper

For a one dimensional diffusion process $X=\{X(t) ; 0\leq t \leq T \}$, we suppose that $X(t)$ is hidden if it is below some fixed and known threshold $\tau$, but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is to estimate 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 $h_n$ such that $n h_n=T$. The asymptotic is when $h_n\to0$, $T\to\infty$ and $n h_n^2\to 0$ as $n\to\infty$. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved.

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