Krzysztof Bisewski

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20192022

most citedRare Event Simulation for Steady-State Probabilities via Recurrency Cycles

2 citations · 3 across the 5 of their papers we have counts for

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math.PR2022

Lower bound for the expected supremum of fractional Brownian motion using coupling

Krzysztof Bisewski

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 horizon. Extensive simulat…

math.PR2021★ 1 cited

Simultaneous ruin probability for multivariate gaussian risk model

Krzysztof Bisewski, Krzysztof Debicki, Nikolai Kriukov

Let $Z (t) = (Z_{1} (t), \dots, Z_{d} (t))^{⊤}, t \in R$ where $Z_{i} (t), t \in R$ , $i = 1, ..., d$ are mutually independent centered Gaussian processes with continuo…

math.PR2021

Derivatives of sup-functionals of fractional Brownian motion evaluated at H=1/2

Krzysztof Bisewski, Krzysztof Dębicki, Tomasz Rolski

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: expected value of the…

math.PR2019★ 2 cited

Rare Event Simulation for Steady-State Probabilities via Recurrency Cycles

Krzysztof Bisewski, Daan Crommelin, Michel Mandjes

We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $R^{d}$ …