Estimation of parameters for diffusion processes with jumps from discrete observations

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 _i ⁿ = ih _n, 0 ≤ i ≤ n. We suppose h _n → 0, nh _n → ∞, nh _n ² → 0.