Journal article

The Rate Of Convergence For Euler Approximations Of Solutions Of Stochastic Differential Equations Driven By Fractional Brownian Motion

Year:

2008

Published in:

Stochastics
Euler approximations
stochastic differential equations
fractional Brownian motion
fractional white noise
rate of convergence

The paper focuses on discrete-type approximations of solutions to non-homogeneous stochastic differential equations (SDEs) involving fractional Brownian motion (fBm). We prove that the rate of convergence for Euler approximations of solutions of pathwise SDEs driven by fBm with Hurst index 

Other publications by

74 publications found

2025
Journal article

Stochastic Selection Problem For A Stratonovich Sde With Power Non‑Linearity

Publisher: Bernoulli

Authors: Georgiy Shevchenko, Ilya Pavlyukevich

2014
Working paper

Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2018
Working paper

Existence And Uniqueness Of Mild Solution To Stochastic Heat Equation With White And Fractional Noises

Publisher: arxiv

Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura

2013
Journal article

Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations

Publisher: Statistics & Probability Letters

Authors: Georgiy Shevchenko, Taras Shalaiko

2014
Book Chapter

On The Distribution Of Integral Functionals Of A Homogeneous Diffusion Process

Publisher: Bocconi & Springer Series

Authors: Georgiy Shevchenko, M. Perestyuk, Yulia Mishura

2011
Journal article

Existence And Uniqueness Of The Solution Of Stochastic Differential Equation Involving Wiener Process And Fractional Brownian Motion With Hurst Index H > 1/2

Publisher: Communications in Statistics - Theory and Methods

Authors: Georgiy Shevchenko, Yulia Mishura

2015
Journal article

Asymptotic Behavior Of Mixed Power Variations And Statistical Estimation In Mixed Models

Publisher: Statistical Inference for Stochastic Processes

Authors: Georgiy Shevchenko, Yulia Mishura, Marco Dozzi

2011
Journal article

Real Harmonizable Multifractional Stable Process And Its Local Properties

Publisher: Stochastic Processes and their Applications

Authors: Georgiy Shevchenko, Marco Dozzi, Yulia Mishura, Kostiantyn Ral’chenko

2015
Journal article

Convergence Of Solutions Of Mixed Stochastic Delay Differential Equations With Applications

Publisher: Applied Mathematics and Computation

Authors: Georgiy Shevchenko, Yulia Mishura, Taras Shalaiko

2009
Book Chapter

The Optimal Time To Exchange One Asset For Another On Finite Interval

Publisher: Springer Berlin

Authors: Georgiy Shevchenko, Yulia Mishura