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

Daniel Harnett and David Nualart

Stochastic Processes and their Applications, 2018, vol. 128, issue 2, 404-425

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.

Keywords: Central limit theorem; Breuer–Major theorem; Fourth Moment Theorem; Self-similar processes (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:2:p:404-425

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DOI: 10.1016/j.spa.2017.04.014

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