# Extremes of γ-reflected Gaussian processes with stationary increments

## Détails

ID Serval
serval:BIB_113D6DBB556B
Type
Article: article d'un périodique ou d'un magazine.
Collection
Publications
Institution
Titre
Extremes of γ-reflected Gaussian processes with stationary increments
Périodique
ESAIM: Probability and Statistics
ISSN
1292-8100
1262-3318
Statut éditorial
Publié
Date de publication
2017
Peer-reviewed
Oui
Volume
21
Pages
495-535
Langue
anglais
Résumé
For a given centered Gaussian process with stationary increments $\{X(t), t\geq 0\}$ and $c>0$, let $$W_\gamma(t)=X(t)-ct-\gamma\inf_{0\leq s\leq t}\left(X(s)-cs\right), \quad t\geq 0$$ denote the $\gamma$-reflected process, where $\gamma\in (0,1)$. This process is introduced in the context of risk theory to model surplus process that include tax payments of loss-carry forward type.In this contribution we derive asymptotic approximations of both the ruin probability and the joint distribution of first and last passage times given that ruin occurs. We apply our findings to the cases with $X$ being the multiplex fractional Brownian motion and the integrated Gaussian processes. As a by-product we derive an extension of Piterbarg inequality \KD{for} threshold-dependent random fields.

Mots-clé
Statistics and Probability, Statistics and Probability, Statistics and Probability
Création de la notice
11/11/2017 13:26
Dernière modification de la notice
21/08/2019 6:17
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