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Extremes of threshold-dependent Gaussian processes
- Publication Year :
- 2017
-
Abstract
- In this contribution we are concerned with the asymptotic behaviour as $u\to \infty$ of $\mathbb{P}\{\sup_{t\in [0,T]} X_u(t)> u\}$, where $X_u(t),t\in [0,T],u>0$ is a family of centered Gaussian processes with continuous trajectories. A key application of our findings concerns $\mathbb{P}\{\sup_{t\in [0,T]} (X(t)+ g(t))> u\}$ as $u\to\infty$, 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.<br />Comment: 28 pages
- Subjects :
- Mathematics - Probability
Mathematics - Statistics Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1701.05387
- Document Type :
- Working Paper