Electronic Journal of Probability

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

Daniel Dobbs and Tai Melcher

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Small deviations homogeneous chaos

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


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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