Estimation of parameters for diffusion processes with jumps from discrete observations

Yasutaka Shimizu, Nakahiro Yoshida

Research output: Contribution to journalArticle

60 Citations (Scopus)

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 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
Volume9
Issue number3
DOIs
Publication statusPublished - 2006 Oct
Externally publishedYes

Fingerprint

Discrete Observations
Diffusion Process
Jump
Poisson Random Measure
Compound Poisson Process
Discrete Data
Term
Diffusion Coefficient
Coefficient

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Estimation of parameters for diffusion processes with jumps from discrete observations. / Shimizu, Yasutaka; Yoshida, Nakahiro.

In: Statistical Inference for Stochastic Processes, Vol. 9, No. 3, 10.2006, p. 227-277.

Research output: Contribution to journalArticle

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