Estimation of parameters for diffusion processes with jumps from discrete observations

Yasutaka Shimizu*, Nakahiro Yoshida

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

90 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)227-277
Number of pages51
JournalStatistical Inference for Stochastic Processes
Issue number3
Publication statusPublished - 2006 Oct
Externally publishedYes


  • Asymptotic efficiency
  • Asymptotic normality
  • Contrast function
  • Diffusion process with jumps
  • Discrete observation
  • Parametric inference

ASJC Scopus subject areas

  • Statistics and Probability


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