Large deviations for functionals of some self-similar Gaussian processes

2018/02/12 by Song, Xiaoming · 1 citation
#60F10 #60G15 #60G18 #60G22 #60J55 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.04224

Abstract

We prove large deviation principles for ∫₀^t γ(X_s)ds, where X is a d-dimensional self-similar Gaussian process and γ(x) takes the form of the Dirac delta function δ(x), |x|^-β with β∈ (0,d), or ∏_i=1^d |x_i|^-β_i with β_i∈(0,1). In particular, large deviations are obtained for the functionals of d-dimensional fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. As an application, the critical exponential integrability of the functionals is discussed.

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• On the passage times of self-similar Gaussian processes on curved boundaries

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