Stochastic Analysis of Mixed Fractional Gaussian Processes - 1st Edition - ISBN: 9781785482458

Stochastic Analysis of Mixed Fractional Gaussian Processes

1st Edition

Authors: Yuliya Mishura Mounir Zili
Hardcover ISBN: 9781785482458
Imprint: ISTE Press - Elsevier
Published Date: 1st May 2018
Page Count: 200
Sales tax will be calculated at check-out Price includes VAT/GST

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Description

Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts.

Key Features

  • Presents both mixed fractional and sub-fractional Brownian motions
  • Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students
  • Includes different Hurst indices

Readership

Master's and Phd students and researchers specializing in statistics, stochastics and finances

Table of Contents

Chapter 1. Gaussian processes  (30 pages)
1.1  Gaussian vectors
1.2 Gaussian processes and their characterizations
1.3  Wiener process and related properties
        1.3.1 Classical properties
        1.3.2 Regularity of the paths and their Hausdorff dimension
Chapter 2. Fractional Brownian motion (30 pages)
  2.1 Definition and Existence
  2.2 Self-similarity
  2.3 Stationarity and range dependence of increments
  2.4 Power variations
  2.5  Hausdorff dimension of paths
Chapter 3. Mixed and sub-mixed fractional Brownian motions (50 pages)
  3.1 Definition and basic properties
  3.2 Mixed-self similarity
  3.3 Short range dependence of increments
  3.4 Hausdorff dimension of the graphs and the trajectories
  3.5 Study of semi-martingale property
Chapter 4.  Stochastic integration w.r.t. mixed fractional Gaussian processes (40 pages)
 4.1 Integration of nonrandom functions
 4.2 Pathwise integration
4.3 Wick integration
Chapter 5.  Stochastic differential equations driven by mixed fractional Gaussian processes (50 pages)
 5.1 Existence and uniqueness of the solution of the SDE driven by a mixed and sub-mixed fractional Brownian motion
 5.2 Statistical estimates for the SDE involving mixed and sub-mixed fBms and uknown parameters
 5.3 Some financial applications of the mixed models

Details

No. of pages:
200
Copyright:
© ISTE Press - Elsevier 2018
Published:
Imprint:
ISTE Press - Elsevier
Hardcover ISBN:
9781785482458

About the Author

Yuliya Mishura

Yuliya Mishura is Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. Her research interests include stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, and models with long-range dependence.

Affiliations and Expertise

Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev, Ukraine

Mounir Zili

Mounir Zili works at the University of Monastir, Faculty of sciences of Monastir with expertise in Probability Theory, Applied Mathematics, Analysis

Affiliations and Expertise

Professor, Faculty of Sciences, Monastir-University of Monastir

Ratings and Reviews