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Expansion of Lévy Process Functionals and its Application in Statistical Estimation

89 Pages Posted: 22 Mar 2012  

Jiti Gao

Monash University - Department of Econometrics & Business Statistics

Chaohua Dong

Southwestern University of Finance and Economics

Date Written: March, 22 2012

Abstract

In this paper, expansions of functionals of Lévy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Lévy processes are considered. Several expansions and rates of convergence are established. In order to state asymptotic distributions for statistical estimators of unknown parameters involved in a general regression model, we develop a general asymptotic theory for partial sums of functionals of Lévy processes. The results show that these estimators of the unknown parameters in different situations converge to quite different random variables. In addition, the rates of convergence depend on various factors rather than just the sample size.

Keywords: expansions, Lévy Process, Orthogonal Series, Statistical Estimation

JEL Classification: C13, C14, C22

Suggested Citation

Gao, Jiti and Dong, Chaohua, Expansion of Lévy Process Functionals and its Application in Statistical Estimation (March, 22 2012). Available at SSRN: https://ssrn.com/abstract=2027272 or http://dx.doi.org/10.2139/ssrn.2027272

Jiti Gao (Contact Author)

Monash University - Department of Econometrics & Business Statistics ( email )

900 Dandenong Road
Caulfield East, Victoria 3145
Australia
61399031675 (Phone)
61399032007 (Fax)

HOME PAGE: http://www.jitigao.com

Chaohua Dong

Southwestern University of Finance and Economics ( email )

555 Liutai Avenue
Wenjiang District
Chengdu, Sichuan 611130
China

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