Working paper

Fractional Brownian Motion In A Nutshell

Year:

2014

Published in:

arxiv
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.

Other publications by

67 publications found

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

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

Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion

Publisher: Random Operators and Stochastic Equations

Authors: Georgiy Shevchenko, Yulia Mishura

2013
Journal article

Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations

Publisher: Statistics & Probability Letters

Authors: Georgiy Shevchenko, Taras Shalaiko

2016
Journal article

Stochastic Wave Equation In A Plane Driven By Spatial Stable Noise

Publisher: Modern Stochastics: Theory and Applications

Authors: Georgiy Shevchenko, Larysa Pryhara

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

2007
Journal article

Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

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

2022
Journal article

Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva

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