Let X (t), t∈ ℝd, be a centered Gaussian random field with continuous trajectories and set ξu
(t)= X (f (u) t), t∈ ℝd, with f some positive function. Using classical results we can establish …

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 …

For a given centered Gaussian process with stationary increments X (t), t≥ 0 and c> 0, let W
γ (t)= X (t)− ct− γinf 0≤ s≤ t (X (s)− cs), t≥ 0 denote the γ-reflected process, where γ∈(0, 1) …

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 …

Gaussian random fields on Euclidean spaces whose variances reach their maximum values
at unique points are considered. Exact asymptotic behaviors of probabilities of large …

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 …

Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we
derive the asymptotics of P sup x∈[0, 1] n W (x)| W (1)= w> u, w∈ R, for large u, where W (x) …

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 …

Gaussian random processes which variances reach theirs maximum values at unique points
are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of …

We study the asymptotics of the classical fractional Brownian ruin model with random time
inspection governed by an independent non-negative pure jumps Lévy process. Formally …