数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 645-663.doi: 10.1016/S0252-9602(10)60067-7

• 论文 •    下一篇

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

龙红卫   

  1. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, |Florida 33431-0991, USA
  • 收稿日期:2009-09-05 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    This work is supported by FAU Start-up funding at the C. E. Schmidt College of Science

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

Long Hongwei   

  1. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, |Florida 33431-0991, USA
  • Received:2009-09-05 Online:2010-05-20 Published:2010-05-20
  • Supported by:

    This work is supported by FAU Start-up funding at the C. E. Schmidt College of Science

摘要:

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points ti=i/n, i=1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator(LSE) when a small dispersion parameter ε→0 and n → ∝simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

关键词: Asymptotic distribution of LSE, consistency of LSE, discrete observations, least squares method, parameter estimation, small α-stable noises, stable distribution, stochastic differential equations

Abstract:

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points ti=i/n, i=1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator(LSE) when a small dispersion parameter ε→0 and n → ∝simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

Key words: Asymptotic distribution of LSE, consistency of LSE, discrete observations, least squares method, parameter estimation, small α-stable noises, stable distribution, stochastic differential equations

中图分类号: 

  • 60G52