Central limit theorem for functionals of a generalized self-similar Gaussian process

2015/08/11 by Harnett, Daniel, Nualart, David
#60F05 #60G18 #60H07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1508.02756

Abstract

We consider a class of self-similar, continuous Gaussian processes that do not necessarily have stationary increments. We prove a version of the Breuer-Major theorem for this class, that is, subject to conditions on the covariance function, a generic functional of the process increments converges in law to a Gaussian random variable. The proof is based on the Fourth Moment Theorem. We give examples of five non-stationary processes that satisfy these conditions.

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