### 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 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Statistical Inference for Stochastic Processes*, vol. 9, no. 3, pp. 227-277. https://doi.org/10.1007/s11203-005-8114-x

}

TY - JOUR

T1 - Estimation of parameters for diffusion processes with jumps from discrete observations

AU - Shimizu, Yasutaka

AU - Yoshida, Nakahiro

PY - 2006/10

Y1 - 2006/10

N2 - 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.

AB - 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.

KW - Asymptotic efficiency

KW - Asymptotic normality

KW - Contrast function

KW - Diffusion process with jumps

KW - Discrete observation

KW - Parametric inference

UR - http://www.scopus.com/inward/record.url?scp=33745893839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745893839&partnerID=8YFLogxK

U2 - 10.1007/s11203-005-8114-x

DO - 10.1007/s11203-005-8114-x

M3 - Article

AN - SCOPUS:33745893839

VL - 9

SP - 227

EP - 277

JO - Statistical Inference for Stochastic Processes

JF - Statistical Inference for Stochastic Processes

SN - 1387-0874

IS - 3

ER -