Electronic Journal of Probability

Small deviations for time-changed Brownian motions and applications to second-order chaos

Daniel Dobbs and Tai Melcher

Full-text: Open access

Abstract

We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous chaos.

Article information

Source
Electron. J. Probab. Volume 19 (2014), paper no. 85, 23 pp.

Dates
Accepted: 16 September 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
http://projecteuclid.org/euclid.ejp/1465065727

Digital Object Identifier
doi:10.1214/EJP.v19-2993

Mathematical Reviews number (MathSciNet)
MR3263642

Zentralblatt MATH identifier
1329.60087

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G51: Processes with independent increments; Lévy processes 60F17: Functional limit theorems; invariance principles

Keywords
Small deviations homogeneous chaos

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Dobbs, Daniel; Melcher, Tai. Small deviations for time-changed Brownian motions and applications to second-order chaos. Electron. J. Probab. 19 (2014), paper no. 85, 23 pp. doi:10.1214/EJP.v19-2993. http://projecteuclid.org/euclid.ejp/1465065727.


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