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Small deviations for time-changed Brownian motions and applications to second-order chaos. (English) Zbl 1329.60087
Summary: 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.
MSC:
60F99 Limit theorems in probability theory
60F10 Large deviations
60J65 Brownian motion
60H05 Stochastic integrals
60G15 Gaussian processes
60G51 Processes with independent increments; Lévy processes
60F17 Functional limit theorems; invariance principles
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