Working paper

Fractional Brownian Motion In A Nutshell

Year:

2014

Published in:

arxiv

Authors:

Fractional Brownian motion (fBm)

Hurst parameter

Self-similarity

Stationarity of increments

Simulation algorithm

This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.

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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

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

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

2008

Journal article

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

Publisher: Stochastics

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