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.

• 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

• Front Cover 2
• Stochastic Analysis of Mixed Fractional Gaussian Processes 5
• Copyright 6
• Contents 7
• Preface 11
• Introduction 13
• 1. Gaussian Processes 19
  • 1.1. Some preliminaries 19
  • 1.2. Gaussian variables and vectors 20
  • 1.3. Gaussian processes 28
  • 1.4. Exercises 46
• 2. Fractional and Sub-fractional Brownian Motions 49
  • 2.1. Fractional Brownian motion 49
  • 2.2. Sub-fractional Brownian motion 51
  • 2.3. Longand short-range dependence of fBm and sfBm 61