Search Results - "Dȩbicki, Krzysztof"

Extremes of reflecting Gaussian processes on discrete grid by Dȩbicki, Krzysztof, Jasnovidov, Grigori

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Approximation of Supremum of Max-Stable Stationary Processes & Pickands Constants by Dȩbicki, Krzysztof, Hashorva, Enkelejd

“…Let X ( t ) , t ∈ R be a stochastically continuous stationary max-stable process with Fréchet marginals Φ α , α > 0 and set M X ( T ) = sup t ∈ [ 0 , T ] X ( t…”
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Generalized Pickands constants and stationary max-stable processes by Dȩbicki, Krzysztof, Engelke, Sebastian, Hashorva, Enkelejd

“…Pickands constants play a crucial role in the asymptotic theory of Gaussian processes. They are commonly defined as the limits of a sequence of expectations…”
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Exact asymptotics of component-wise extrema of two-dimensional Brownian motion by Dȩbicki, Krzysztof, Ji, Lanpeng, Rolski, Tomasz

“…We derive the exact asymptotics of ℙ sup t ≥ 0 X 1 ( t ) − μ 1 t > u , sup s ≥ 0 X 2 ( s ) − μ 2 s > u , u → ∞ , where ( X 1 ( t ), X 2 ( s )) t , s ≥ 0 is a…”
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Pandemic-type failures in multivariate Brownian risk models by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Kriukov, Nikolai

“…Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of…”
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EXTREMES OF A CLASS OF NONHOMOGENEOUS GAUSSIAN RANDOM FIELDS by Dębicki, Krzysztof, Hashorva, Enkelejd, Ji, Lanpeng

“…This contribution establishes exact tail asymptotics of sup(s,t)∈E X(s, t) for a large class of nonhomogeneous Gaussian random fields X on a bounded convex set…”
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On Generalised Piterbarg Constants by Bai, Long, Dȩbicki, Krzysztof, Hashorva, Enkelejd, Luo, Li

“…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…”
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The time of ultimate recovery in Gaussian risk model by Dȩbicki, Krzysztof, Liu, Peng

“…We analyze the distance R T ( u ) between the first and the last passage time of { X ( t ) − c t : t ∈ [0, T ]} at level u in time horizon T ∈ (0, ∞ ], where X…”
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Simultaneous ruin probability for multivariate Gaussian risk model by Bisewski, Krzysztof, Dȩbicki, Krzysztof, Kriukov, Nikolai

“…Let Z(t)=(Z1(t),…,Zd(t))⊤,t∈R where Zi(t),t∈R, i=1,…,d are mutually independent centered Gaussian processes with continuous sample paths a.s. and stationary…”
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Approximation of Sojourn Times of Gaussian Processes by Dȩbicki, Krzysztof, Michna, Zbigniew, Peng, Xiaofan

“…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…”
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Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics by Dȩbicki, Krzysztof, Ji, Lanpeng, Novikov, Svyatoslav

“…For { B H ( t ) = ( B H , 1 ( t ) , … , B H , d ( t ) ) ⊤ , t ≥ 0 } , where { B H , i ( t ) , t ≥ 0 } , 1 ≤ i ≤ d are mutually independent fractional Brownian…”
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Editorial introduction: special issue on Gaussian queues by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Mandjes, Michel

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Sojourns of fractional Brownian motion queues: transient asymptotics by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Liu, Peng

“…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 ,…”
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Finite-time ruin probability for correlated Brownian motions by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Krystecki, Konrad

“…Let be a two-dimensional Gaussian process with standard Brownian motion marginals and constant correlation . Define the joint survival probability of both…”
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Sojourn Times of Gaussian Processes with Trend by Dȩbicki, Krzysztof, Liu, Peng, Michna, Zbigniew

“…We derive exact tail asymptotics of sojourn time above the level u ≥ 0 P v ( u ) ∫ 0 T I ( X ( t ) - c t > u ) d t > x , x ≥ 0 , as u → ∞ , where X is a…”
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On Berman Functions by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Michna, Zbigniew

“…Let Z ( t ) = exp 2 B H ( t ) - t 2 H , t ∈ R with B H ( t ) , t ∈ R a standard fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 0 , 1 ] and define…”
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Extremes of Gaussian random fields with regularly varying dependence structure by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Liu, Peng

“…Let 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 , and let M ( 𝓣…”
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Derivative of the expected supremum of fractional Brownian motion at H=1 by Bisewski, Krzysztof, Dȩbicki, Krzysztof, Rolski, Tomasz

“…The H -derivative of the expected supremum of fractional Brownian motion { B H ( t ) , t ∈ R + } with drift a ∈ R over time interval [0,  T ] ∂ ∂ H E ( sup t ∈…”
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Simultaneous ruin probability for two-dimensional brownian risk model by Dȩbicki, Krzysztof, Hashorva, Enkelejd, Michna, Zbigniew

“…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…”
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Extremes of nonstationary Gaussian fluid queues by Dȩbicki, Krzysztof, Liu, Peng

“…We investigate the asymptotic properties of the transient queue length process Q(t)=max(Q(0)+X(t)-ct, sup0≤s≤t(X(t)-X(s)-c(t-s))), t≥0, in the Gaussian fluid…”
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