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Invariance principle, multifractional Gaussian processes and long-range dependence

Serge Cohen·Renaud Marty
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Abstract

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional Brownian motion.

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Serge Cohen, Renaud Marty. 2008-06-30. Invariance principle, multifractional Gaussian processes and long-range dependence. https://doi.org/10.1214/07-aihp127

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