Small Deviations for Time-Changed Brownian Motions and Applications to Second-Order Chaos

2013/09/03 by Daniel Dobbs, Dobbs, Daniel, Tai Melcher +1
Economics, Econometrics and Finance · Mathematics · #60 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60

paper · pdf · doi:10.48550/arxiv.1309.0705

23 pages

openalex publication_date 2013/09/03 · arxiv created 2016/11/11 · arxiv updated 2016/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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