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

作者：Harnett Daniel^*; Nualart David

来源：Stochastic Processes and Their Applications, 2018, 128(2): 404-425.

DOI：10.1016/j.spa.2017.04.014

• Central limit theorem
• Breuer-Major theorem
• Fourth Moment Theorem
• Self-similar processes

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.

• 出版日期2018-2