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07/10/2023
On the randomized Euler algorithm under inexact information
This paper focuses on analyzing the error of the randomized Euler algori...
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06/15/2023
On approximation of solutions of stochastic delay differential equations via randomized Euler scheme
We investigate existence, uniqueness and approximation of solutions to s...
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03/10/2023
Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift
In this note we prove sharp lower error bounds for numerical methods for...
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12/01/2022
Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs
We investigate the error of the randomized Milstein algorithm for solvin...
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11/16/2022
A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient
We present the first higher-order approximation scheme for solutions of ...
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09/15/2022
Euler scheme for approximation of solution of nonlinear ODEs under inexact information
We investigate error of the Euler scheme in the case when the right-hand...
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08/10/2022
Foundations of Monte Carlo methods and stochastic simulations – From Monte Carlo Lebesgue integration to weak approximation of SDEs
In recent years dynamical systems (of deterministic and stochastic natur...
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06/07/2022
Monte Carlo integration with adaptive variance reduction: an asymptotic analysis
The crude Monte Carlo approximates the integral S(f)=∫_a^b f(x) dx ...
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04/26/2022
On automatic calibration of the SIRD epidemiological model for COVID-19 data in Poland
We propose a novel methodology for estimating the epidemiological parame...
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04/05/2022
Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations
In this paper we address the existence, uniqueness and approximation of ...
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08/05/2021
Efficient approximation of SDEs driven by countably dimensional Wiener process and Poisson random measure
In this paper we deal with pointwise approximation of solutions of stoch...
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06/07/2021
Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme
We deal with approximation of solutions of delay differential equations ...
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04/30/2021
On the randomized Euler schemes for ODEs under inexact information
We analyse errors of randomized explicit and implicit Euler schemes for ...
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11/17/2020
On mathematical aspects of evolution of dislocation density in metallic materials
This paper deals with the solution of delay differential equations descr...
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06/22/2020
Randomized Runge-Kutta method – stability and convergence under inexact information
We deal with optimal approximation of solutions of ODEs under local Lips...
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12/14/2019
Randomized derivative-free Milstein algorithm for efficient approximation of solutions of SDEs under noisy information
We deal with pointwise approximation of solutions of scalar stochastic d...
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12/09/2019