Estimation of Parameters for Diffusion Processes with Jumps from Discrete Observations

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 coeffi- cient, b(x, σ ) be a diffusion coefficient respectively, and the jump term is driven by a Pois- son 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 + 1d ata att n i = ihn, 0 i n. We suppose hn → 0 ,n h n →∞ ,n h 2 n → 0.