Symmetric stochastic integrals with respect to a class of self-similar Gaussian processes

2017/06/13 by Harnett, Daniel, Jaramillo, Arturo, Nualart, David
#60G18 #60G22 #60H05 #60H07 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1706.03890

Abstract

We study the asymptotic behavior of the ν-symmetric Riemman sums for functionals of a self-similar centered Gaussian process X with increment exponent 0(2ℓ+1)^-1, we prove that the convergence holds in probability.

Related

• Limit theorems for functionals of Gaussian vectors
• Central limit theorem for functionals of a generalized self-similar Gaussian process
• Weak symmetric integrals with respect to the fractional Brownian motion
• Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes
• Decomposition and limit theorems for a class of self-similar Gaussian processes