Articles

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

  • Long Hongwei
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  • Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, |Florida 33431-0991, USA

Received date: 2009-09-05

  Online published: 2010-05-20

Supported by

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

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.

Cite this article

Long Hongwei . PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 645 -663 . DOI: 10.1016/S0252-9602(10)60067-7

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