Electronic Journal of Probability

Quadratic Variations along Irregular Subdivisions for Gaussian Processes

Arnaud Begyn

Full-text: Open access

Abstract

In this paper we deal with second order quadratic variations  along general  subdivisions for processes with Gaussian increments. These have almost surely a deterministic limit under conditions on the mesh of the subdivisions. This limit depends on the singularity function of the process and on the structure of the subdivisions too. Then we illustrate the results with the example of the time-space deformed fractional Brownian motion and we present some simulations.

Article information

Source
Electron. J. Probab., Volume 10 (2005), paper no. 20, 691-717.

Dates
Accepted: 13 July 2005
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464816821

Digital Object Identifier
doi:10.1214/EJP.v10-245

Mathematical Reviews number (MathSciNet)
MR2164027

Zentralblatt MATH identifier
1109.60024

Subjects
Primary: 60F15: Strong theorems 60G15: Gaussian processes
Secondary: 60G17: Sample path properties 60G18: Self-similar processes

Keywords
estimation fractional processes Gaussian processes generalized quadratic variations irregular subdivisions singularity function

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Begyn, Arnaud. Quadratic Variations along Irregular Subdivisions for Gaussian Processes. Electron. J. Probab. 10 (2005), paper no. 20, 691--717. doi:10.1214/EJP.v10-245. https://projecteuclid.org/euclid.ejp/1464816821


Export citation