Limit theorems for functionals of two independent Gaussian processes

2017/11/29 by Jian Song, Song, Jian, Fangjun Xu +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1711.10642

openalex publication_date 2017/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citenx1 and a paring technique are employed.

Related

• Limit theorems for additive functionals of some self-similar Gaussian processes
• Weak convergence towards two independent Gaussian processes from a unique Poisson process
• Limit theorem and LIL for some additive functionals associated to fBm and Riemann-Liouiville process
• Central limit theorem for functionals of two independent fractional Brownian motions
• Weak approximation for Gaussian processes from renewal processes