14 citations · 85 across the 25 of their papers we have counts for
21 papers · 1 filter
Error of randomized Milstein scheme for scalar SDEs with noisy information about coefficients and Wiener process
Paweł M. Morkisz, Paweł Przybyłowicz, Martyna Wiącek
We investigate the strong approximation of scalar stochastic differential equations when the available standard information about the drift coefficient, the diffusion coefficient,…
On the error of the Euler scheme for approximation of solutions of nonlinear DDEs under inexact information
Paweł Przybyłowicz, Martyna Wiącek
We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by…
On the randomized Euler scheme for SDEs with integral-form drift
Paweł Przybyłowicz, Michał Sobieraj
In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form.…
On the randomized Euler algorithm under inexact information
Marcin Baranek, Andrzej Kałuża, Paweł M. Morkisz +2
This paper focuses on analyzing the error of the randomized Euler algorithm when only noisy information about the coefficients of the underlying stochastic differential equation (S…
On approximation of solutions of stochastic delay differential equations via randomized Euler scheme
Paweł Przybyłowicz, Yue Wu, Xinheng Xie
We investigate existence, uniqueness and approximation of solutions to stochastic delay differential equations (SDDEs) under Carathéodory-type drift coefficients. Moreover, we also…
Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximatio…
Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substa…
A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
Paweł Przybyłowicz, Verena Schwarz, Michaela Szölgyenyi
We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jum…
Euler scheme for approximation of solution of nonlinear ODEs under inexact information
Natalia Czyżewska, Paweł M. Morkisz, Paweł Przybyłowicz
We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz con…
Foundations of Monte Carlo methods and stochastic simulations -- From Monte Carlo Lebesgue integration to weak approximation of SDEs
Paweł Przybyłowicz
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex.…
Monte Carlo integration of functions with adaptive variance reduction: an asymptotic analysis
Leszek Plaskota, Paweł Przybyłowicz, Łukasz Stępień
The theme of the present paper is numerical integration of functions using randomized methods. We consider variance reduction methods that consist in two steps. First the ini…
Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations
Fabio V. Difonzo, Paweł Przybyłowicz, Yue Wu
In this paper we address the existence, uniqueness and approximation of solutions of delay differential equations (DDEs) with Carathéodory type right-hand side functions. We provid…
Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme
Natalia Czyżewska, Paweł M. Morkisz, Paweł Przybyłowicz
We deal with approximation of solutions of delay differential equations (DDEs) via the classical Euler algorithm. We investigate the pointwise error of the Euler scheme under nonst…
On the randomized Euler schemes for ODEs under inexact information
Tomasz Bochacik, Paweł Przybyłowicz
We analyse errors of randomized explicit and implicit Euler schemes for approximate solving of ordinary differential equations (ODEs). We consider classes of ODEs for which the rig…
On mathematical aspects of evolution of dislocation density in metallic materials
Natalia Czyżewska, Jan Kusiak, Paweł Morkisz +5
This paper deals with the solution of delay differential equations describing evolution of dislocation density in metallic materials. Hardening, restoration, and recrystallization…
Randomized Runge-Kutta method -- stability and convergence under inexact information
Tomasz Bochacik, Maciej Goćwin, Paweł M. Morkisz +1
We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the rando…
Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information
Paweł M. Morkisz, Paweł Przybyłowicz
We deal with pointwise approximation of solutions of scalar stochastic differential equations in the presence of informational noise about underlying drift and diffusion coefficien…
Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift
Paweł Przybyłowicz, Michaela Szölgyenyi
In this paper we study jump-diffusion stochastic differential equations (SDEs) with a discontinuous drift coefficient and a possibly degenerate diffusion coefficient. Such SDEs app…
Optimal approximation of stochastic integrals in analytic noise model
Andrzej Kałuża, Paweł M. Morkisz, Paweł Przybyłowicz
We study approximate stochastic Itô integration of processes belonging to a class of progressively measurable stochastic processes that are Hölder continuous in the th mean. Ins…
Efficient finite-dimensional solution of initial value problems in infinite-dimensional Banach spaces
Boleslaw Kacewicz, Pawel Przybylowicz
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in t…
Optimal sampling design for global approximation of jump diffusion SDEs
Paweł Przybyłowicz
The paper deals with strong global approximation of SDEs driven by two independent processes: a nonhomogeneous Poisson process and a Wiener process. We assume that the jump and dif…