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From Hermite Polynomials to Multifractional Processes

Part of:Stochastic processesLimit theorems

Published online by Cambridge University Press:  30 January 2018

Renaud Marty
Renaud Marty*
Affiliation:
Université de Lorraine
*
∗ Postal address: Institut Élie Cartan, Université de Lorraine, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France. Email address: renaud.marty@univ-lorraine.fr
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Abstract

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We consider a class of multifractional processes related to Hermite polynomials. We show that these processes satisfy an invariance principle. To prove the main result of this paper, we use properties of the Hermite polynomials and the multiple Wiener integrals. Because of the multifractionality, we also need to deal with variations of the Hurst index by means of some uniform estimates.

Keywords

Multifractional processHermite polynomiallimit theoremsample path properties

MSC classification

Primary:60F17: Functional limit theorems; invariance principles60G17: Sample path properties60G22: Fractional processes, including fractional Brownian motion

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013, pp. 323 - 343
Copyright
© Applied Probability Trust 

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