Journal of Applied Probability

From Hermite polynomials to multifractional processes

Renaud Marty

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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.

Article information

J. Appl. Probab., Volume 50, Number 2 (2013), 323-343.

First available in Project Euclid: 19 June 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60G17: Sample path properties 60G22: Fractional processes, including fractional Brownian motion

Multifractional process Hermite polynomial limit theorem sample path properties


Marty, Renaud. From Hermite polynomials to multifractional processes. J. Appl. Probab. 50 (2013), no. 2, 323--343. doi:10.1239/jap/1371648944.

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