Limit theorems for functionals of two independent Gaussian processes

Jian Song, Fangjun Xu and Qian Yu

Stochastic Processes and their Applications, 2019, vol. 129, issue 11, 4791-4836

Abstract: Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. A new and interesting phenomenon is that, in comparison with the results for fractional Brownian motion, extra randomness appears in the limiting distributions for Gaussian processes with nonstationary increments, say sub-fractional Brownian motion and bi-fractional Brownian. The results are obtained based on the method of moments, in which Fourier analysis, the chaining argument introduced in [11] and a pairing technique are employed.

Keywords: Limit theorem; Gaussian processes; Method of moments; Chaining argument; Pairing technique (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.12.014

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