5 citations · 9 across the 7 of their papers we have counts for
15 papers · 1 filter
On Berman functions
Krzysztof Dębicki, Enkelejd Hashorva, Zbigniew Michna
For fractional Brownian motion with Hurst parameter H the Berman constant is defined. In this paper we consider a general random field (rf) Z that is a spectral rf of some stationa…
Simultaneous ruin probability for multivariate gaussian risk model
Krzysztof Bisewski, Krzysztof Debicki, Nikolai Kriukov
Let where , are mutually independent centered Gaussian processes with continuo…
On the continuity of Pickands constants
Krzysztof Dȩbicki, Enkelejd Hashorva, Zbigniew Michna
For a non-negative separable random field satisfying some mild assumptions we show that \begin{eqnarray*} H_Z^δ= \lim_{T\to\infty} \frac{1}{T^d} E \{\sup_…
Finite-time ruin probability for correlated Brownian motions
Krzysztof Dȩbicki, Enkelejd Hashorva, Konrad Krystecki
Let be a bivariate Brownian motion with standard Brownian motion marginals and constant correlation and define the joint survival probabi…
Exact asymptotics of component-wise extrema of two-dimensional Brownian motion
Krzysztof Debicki, Lanpeng Ji, Tomasz Rolski
We derive the exact asymptotics of \[ P\left( \sup_{t\ge 0} \Bigl( X_1(t) - μ_1 t\Bigr)> u, \ \sup_{s\ge 0} \Bigl( X_2(s) - μ_2 s\Bigr)> u \right), \ \ u\to\infty, \] where $(X_1(t…
Logarithmic asymptotics for probability of component-wise ruin in a two-dimensional Brownian model
Krzysztof Debicki, Lanpeng Ji, Tomasz Rolski
We consider a two-dimensional ruin problem where the surplus process of business lines is modelled by a two-dimensional correlated Brownian motion with drift. We study the ruin fun…