Regularization and integral representations of Hermite processes

It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation wa...

Full description

Saved in:
Bibliographic Details
Published in:Statistics & probability letters 2010-12, Vol.80 (23), p.2014-2023
Main Authors: Pipiras, Vladas, Taqqu, Murad S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fractional Brownian motion
Fractional Brownian motion Hermite processes Multiple Wiener-Ito integrals Stochastic Fubini theorem Regularization
General topics
Hermite processes
Mathematics
Multiple Wiener–Itô integrals
Probability and statistics
Probability theory and stochastic processes
Regularization
Sciences and techniques of general use
Statistics
Stochastic Fubini theorem
Stochastic processes
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation was originally established by using cumulants. The representation was extended to general Hermite processes through the convergence of suitable partial sum processes. We provide here an alternative and different proof for the finite-time interval representation of Hermite processes. The approach is based on regularization of Hermite processes and the fractional Gaussian noises underlying them, and does not use cumulants nor convergence of partial sums.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2010.09.008