### 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 language | English |
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Pages (from-to) | 227-277 |

Number of pages | 51 |

Journal | Statistical Inference for Stochastic Processes |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2006 Oct 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability