Extremes of threshold-dependent Gaussian processes

2017/01/19 by Bai, L., Debicki, K., Hashorva, E. +1
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1701.05387

Abstract

In this contribution we are concerned with the asymptotic behaviour as u→ ∞ of ℙ\sup_{t∈ [0,T]} X_u(t)> u\, where X_u(t),t∈ [0,T],u>0 is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns ℙ\sup_{t∈ [0,T]} (X(t)+ g(t))> u\ as u→∞, for X a centered Gaussian process and g some measurable trend function. Further applications include the approximation of both the ruin time and the ruin probability of the Brownian motion risk model with constant force of interest.

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