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Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations

Authors:	Yasutaka Shimizu Nakahiro Yoshida

Institution:	(1) Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan;(2) Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

Abstract:	In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure q^θ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe n + 1 data at t_iⁿ = ih_n, $0 \leqslant i \leqslant n$ . We suppose h_n → 0, nh_n → ∞, nh_n² → 0. Final version 20 December 2004

Keywords:	diffusion process with jumps parametric inference discrete observation contrast function asymptotic normality asymptotic efficiency
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