Search Results - "Bisewski, Krzysztof"

On the speed of convergence of Piterbarg constants by Bisewski, Krzysztof, Jasnovidov, Grigori

“…In this paper, we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the…”
Get full text

Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid by Bisewski, Krzysztof, Ivanovs, Jevgenijs

Get full text

The harmonic mean formula for random processes by Bisewski, Krzysztof, Hashorva, Enkelejd, Shevchenko, Georgiy

“…Motivated by the classical harmonic mean formula, estabished by Aldous in 1989, we investigate the relation between the sojourn time and supremum of a random…”
Get full text

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…”
Get full text

Derivative of the expected supremum of fractional Brownian motion at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H=1$$\end{document}H=1 by Bisewski, Krzysztof, Dȩbicki, Krzysztof, Rolski, Tomasz

“…The H -derivative of the expected supremum of fractional Brownian motion \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…”
Get full text

Derivatives of sup-functionals of fractional Brownian motion evaluated at H= 12 by Bisewski, Krzysztof, Dȩbicki, Krzysztof, Rolski, Tomasz

Get full text

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 ∈…”
Get full text

SIMULATION-BASED ASSESSMENT OF THE STATIONARY TAIL DISTRIBUTION OF A STOCHASTIC DIFFERENTIAL EQUATION by Bisewski, Krzysztof, Crommelin, Daan, Mandjes, Michel

“…A commonly used approach to analyzing stochastic differential equations (SDEs) relies on performing Monte Carlo simulation with a discrete-time counterpart. In…”
Get full text

Lower bound for the expected supremum of fractional Brownian motion using coupling by Bisewski, Krzysztof

“…We derive a new theoretical lower bound for the expected supremum of drifted fractional Brownian motion with Hurst index $H\in(0,1)$ over (in)finite time…”
Get full text

On the speed of convergence of discrete Pickands constants to continuous ones by Bisewski, Krzysztof, Jasnovidov, Grigori

“…In this manuscript, we address open questions raised by Dieker \& Yakir (2014), who proposed a novel method of estimation of (discrete) Pickands constants…”
Get full text

On the speed of convergence of Piterbarg constants by Bisewski, Krzysztof, Jasnovidov, Grigori

“…In this paper we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the…”
Get full text

Nonparametric testing via partial sorting by Bisewski, Krzysztof, Jansen, H. M, Nazarathy, Yoni

“…In this paper we introduce the idea of partially sorting data to design nonparametric tests. This approach gives rise to tests that are sensitive to both the…”
Get full text

Zooming-in on a L\'evy process: Failure to observe threshold exceedance over a dense grid by Bisewski, Krzysztof, Ivanovs, Jevgenijs

“…Electron. J. Probab. 25: 1-33 (2020) For a L\'evy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$…”
Get full text

Simultaneous ruin probability for multivariate gaussian risk model by Bisewski, Krzysztof, Debicki, Krzysztof, Kriukov, Nikolai

“…Let $\textbf{Z}(t)=(Z_1(t) ,\ldots, Z_d(t))^\top , t \in \mathbb{R}$ where $Z_i(t), t\in \mathbb{R}$, $i=1,...,d$ are mutually independent centered Gaussian…”
Get full text

Derivatives of sup-functionals of fractional Brownian motion evaluated at H=1/2 by Bisewski, Krzysztof, Dębicki, Krzysztof, Rolski, Tomasz

“…We consider a family of sup-functionals of (drifted) fractional Brownian motion with Hurst parameter $H\in(0,1)$. This family includes, but is not limited to:…”
Get full text

The harmonic mean formula for random processes by Bisewski, Krzysztof, Hashorva, Enkelejd, Shevchenko, Georgiy

“…Motivated by the harmonic mean formula in [1], we investigate the relation between the sojourn time and supremum of a random process $X(t),t\in \mathbb{R}^d$…”
Get full text

Bounds for expected supremum of fractional Brownian motion with drift by Bisewski, Krzysztof, Dębicki, Krzysztof, Mandjes, Michel

“…J. Appl. Probab. 58 (2021) 411-427 We provide upper and lower bounds for the mean ${\mathscr M}(H)$ of $\sup_{t\geqslant 0} \{B_H(t) - t\}$, with $B_H(\cdot)$…”
Get full text

Rare Event Simulation for Steady-State Probabilities via Recurrency Cycles by Bisewski, Krzysztof, Crommelin, Daan, Mandjes, Michel

“…Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(3):033131 (2019) We develop a new algorithm for the estimation of rare event probabilities…”
Get full text

Controlling the time discretization bias for the supremum of Brownian Motion by Bisewski, Krzysztof, Crommelin, Daan, Mandjes, Michel

“…ACM Transactions on Modeling and Computer Simulation (TOMACS), 28(3):24 (2018) We consider the bias arising from time discretization when estimating the…”
Get full text