Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals

By Krzysztof Debicki, Enkelejd Hashorva, Lanpeng Ji. 2013

46 citations recorded by the source corpus.

Let {X(t),t ≥ 0} be a centered Gaussian process and let γ be a non-negative constant. In this paper we study the asymptotics of ℙsupt∈[0,T/uγ]X(t)>u$\mathbb {P} \left \{\underset {t\in [0,\mathcal {T}/u^{\gamma }]}\sup X(t)>u\right \}$ as u→∞$u\rightarrow \infty $, with T$\mathcal {T}$ an independent of X non-negative random variable. As an application, we derive the asymptotics of finite-time ruin probability of time-changed fractional Brownian motion risk processes.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/d53085ec183068e4a23550b7f20e822b31b77cab

Citations in the corpus

• Extremes of vector-valued Gaussian processes: exact asymptotics (2015, unknown): “, [1, 8, 26, 29] and the references therein.”