On the randomized Euler algorithm under inexact information

TL;DR

This paper analyzes the error behavior of the randomized Euler algorithm for stochastic differential equations when only noisy data about the coefficients and Wiener process are available, considering different types of disturbances and their regularity effects.

Contribution

It provides a theoretical analysis of the error in the randomized Euler method under inexact information and explores the impact of disturbance regularity on accuracy.

Findings

Error bounds depend on disturbance regularity

Different disturbance classes affect convergence rates

Numerical experiments confirm theoretical predictions

Abstract

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 (SDE) and the driving Wiener process is available. Two classes of disturbed Wiener process are considered, and the dependence of the algorithm's error on the regularity of the disturbing functions is investigated. The paper also presents results from numerical experiments to support the theoretical findings.