English

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

Probability 2016-12-06 v2

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

Cite

@article{arxiv.1508.02756,
  title  = {Central limit theorem for functionals of a generalized self-similar Gaussian process},
  author = {Daniel Harnett and David Nualart},
  journal= {arXiv preprint arXiv:1508.02756},
  year   = {2016}
}
R2 v1 2026-06-22T10:31:37.035Z