We investigate generalised Piterbarg constants P α, δ h= lim T→∞ E sup t∈ δℤ∩[0, T] e 2 B
α (t)−| t| α− h (t) determined in terms of a fractional Brownian motion B α with Hurst index …

The seminal papers of Pickands (Pickands, 1967; Pickands, 1969) paved the way for a
systematic study of high exceedance probabilities of both stationary and non-stationary …

This paper investigates ruin probability and ruin time of a two-dimensional fractional
Brownian motion risk process. The net loss process of an insurance company is modeled by …

We derive exact tail asymptotics of sojourn time above the level u≥ 0 P v (u)∫ 0 TI (X (t)-ct>
u) dt> x, x≥ 0, as u→∞, where X is a Gaussian process with continuous sample paths, c is …

Let X (t), t ∈ RX (t), t∈ R be a stochastically continuous stationary max-stable process with
Fréchet marginals Φ _ α, α> 0 Φ α, α> 0 and set M_X (T)=\sup _ t ∈ 0, TX (t), T> 0 MX (T) …

We investigate the tail asymptotic behavior of the sojourn time for a large class of centered
Gaussian processes X, in both continuous-and discrete-time framework. All results obtained …

Let X (t), t∈ 𝓣 X(t),t∈T be a centered Gaussian random field with variance function σ 2 (⋅)
that attains its maximum at the unique point t 0∈ 𝓣 t_0∈T, and let M (𝓣)= sup t∈ TX (t) …

This paper is concerned with the asymptotic analysis of sojourn times of random fields with
continuous sample paths. Under a very general framework we show that there is an …

In this paper, we are concerned with the asymptotic behavior, as u → ∞ u→∞, of P\left {\sup
_ t ∈ 0, T X_u (t)> u\right\} P supt∈ 0, TX u (t)> u, where X_u (t), t ∈ 0, T, u> 0 X u (t), t∈ 0, T …

We study the asymptotics of sojourn time of the stationary queueing process Q (t), t≥ 0 fed
by a fractional Brownian motion with Hurst parameter H∈(0, 1) above a high threshold u …