13 citations · 55 across the 19 of their papers we have counts for
8 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 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…
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…
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 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…
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…