Small Deviations for Time-Changed Brownian Motions and Applications to Second-Order Chaos
Daniel Dobbs, Tai Melcher
TL;DR
This paper establishes strong small deviation results for time-changed Brownian motions and applies these findings to stochastic integrals within second-order chaos, advancing understanding of their probabilistic behavior.
Contribution
It introduces new small deviation results for time-changed Brownian motions and applies them to second-order chaos integrals, a novel combination in stochastic analysis.
Findings
Strong small deviation results for time-changed Brownian motions.
Application of these results to second-order chaos stochastic integrals.
Enhanced understanding of probabilistic properties of complex stochastic processes.
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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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Mathematical Dynamics and Fractals