21 citations · 43 across the 14 of their papers we have counts for
17 papers
Distributional and Extremal Behaviour of Brownian Motion with Exponential Resetting
Krzysztof Dębicki, Enkelejd Hashorva, Zbigniew Michna
We study the distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting. We obtain an explicit renewal-type formula for the di…
Sojourns of Vector-Valued Stationary Gaussian Random Fields
Krzysztof Dębicki, Enkelejd Hashorva, Zbigniew Michna
For a centered, homogeneous R^d-valued Gaussian random field X(t), t in R^k, with covariance matrix function R(s,t) = E[X(s) X(t)^T], we investigate the exact asymptotics of kappa_…
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…
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_…
Sojourn times of Gaussian related random fields
Krzysztof Dȩbicki, Enkelejd Hashorva, Peng Liu +1
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 interes…
Simultaneous Ruin Probability for Two-Dimensional Brownian and Lévy Risk Models
Krzysztof Dȩbicki, Enkelejd Hashorva, Zbigniew Michna
The ruin probability in the classical Brownian risk model can be explicitly calculated for both finite and infinite-time horizon. This is not the case for the simultaneous ruin pro…
Sojourn times of Gaussian processes with trend
Krzysztof Debicki, Peng Liu, Zbigniew Michna
We derive exact tail asymptotics of sojourn time above the level as , wher…
Ruin probabilities for two collaborating insurance companies
Zbigniew Michna
In this note we find a formula for the supremum distribution of spectrally positive or negative Lévy processes with a broken linear drift. This gives formulas for ruin probabilitie…
Approximation of Sojourn Times of Gaussian Processes
Krzysztof Dȩbicki, Enkelejd Hashorva, Xiaofan Peng +1
We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes , in both continuous- and discrete-time framework. All results o…
The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts
Zbigniew Michna, Stephen M. Disney, Peter Nielsen
We quantify the bullwhip effect (which measures how the variance in replenishment orders is amplified as the orders move up the supply chain) when random demands and random lead ti…
The impact of stochastic lead times on the bullwhip effect
Zbigniew Michna, Peter Nielsen, Izabela Ewa Nielsen
In this article we want to review the research state on the bullwhip effect in supply chains with stochastic lead times and give a contribution to quantifying the bullwhip effect.…
The distribution of the supremum for spectrally asymmetric Lévy processes
Zbigniew Michna, Zbigniew Palmowski, Martijn Pistorius
In this article we derive formulas for the probability and where is a spectrally positive Lévy process with infinit…
The impact of lead time forecasting on the bullwhip effect
Zbigniew Michna, Peter Nielsen
In this article we quantify the bullwhip effect (the variance amplification in replenishment orders) when demands and lead times are predicted in a simple two-stage supply chain wi…
Lévy processes in storage and inventory problems
Zbigniew Michna, Wojciech Bombała, Peter Nielsen
In this paper we consider storage and inventory systems. Our aim is to apply and review main results of the fluctuation theory of stochastic processes in the context of storage and…
Explicit formula for the supremum distribution of a spectrally negative stable process
Zbigniew Michna
In this article we get simple explicit formulas for $\Exp\sup_{s\leq t}X(s)$ where is a spectrally positive or negative Lévy process with infinite variation. As a consequence w…
Formula for the supremum distribution of a spectrally positive Lévy process
Zbigniew Michna
In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where is a spectrally positive Lévy process and $c\in\RL$. As an example we inves…
Remarks on Pickands theorem
Zbigniew Michna
In this article we present Pickands theorem and his double sum method. We follow Piterbarg's proof of this theorem. Since his proof relies on general lemmas we present a complete p…