DeepAI

# 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 side function of the underlying ODE satisfies nonstandard assumptions such as local one-side Lipschitz condition and local Hölder continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Lastly, we present the results of some numerical experiments.

• 3 publications
• 4 publications
• 15 publications
06/07/2021

### Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme

We deal with approximation of solutions of delay differential equations ...
04/30/2021

### On the randomized Euler schemes for ODEs under inexact information

We analyse errors of randomized explicit and implicit Euler schemes for ...
06/07/2022

### Sharp L^1-Approximation of the log-Heston SDE by Euler-type methods

We study the L^1-approximation of the log-Heston SDE at equidistant time...
08/24/2021

### A change of measure enhanced near exact Euler Maruyama scheme for the solution to nonlinear stochastic dynamical systems

The present study utilizes the Girsanov transformation based framework f...
10/01/2020

### Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme

We consider the long-time behavior of an explicit tamed Euler scheme app...
04/11/2017

### Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

In this paper, we propose a symbolic control synthesis method for nonlin...
09/29/2015

### Optimization over Sparse Symmetric Sets via a Nonmonotone Projected Gradient Method

We consider the problem of minimizing a Lipschitz differentiable functio...