Statistical inference for fractional diffusion processes

Statistical inference for fractional diffusion processes / B.L.S. Prakasa Rao.

Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This b...

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Bibliographic Details
Main Author: Rao, B. L. S. Prakasa
Format: eBook
Language:English
Published: Hoboken, N.J. : Wiley, 2013.
Subjects:
Mathematics.
mathematics.
applied mathematics.
MATHEMATICS > Probability & Statistics > General.
Mathematics
Online Access:Click for online access
Table of Contents:
  • ""Table of Contents""; ""Series Page""; ""Title Page""; ""Copyright""; ""Dedication""; ""Preface""; ""Chapter 1: Fractional Brownian Motion and Related Processes""; ""1.1 Introduction""; ""1.2 Self-similar Processes""; ""1.3 Fractional Brownian Motion""; ""1.4 Stochastic Differential Equations Driven by fBm""; ""1.5 Fractional Ornsteinâ€"Uhlenbeck-type Process""; ""1.6 Mixed fBm""; ""1.7 Donsker-type Approximation for fBm with Hurst Index H>1/2""; ""1.8 Simulation of fBm""; ""1.9 Remarks on Application of Modeling by fBm in Mathematical Finance""
  • ""1.10 Pathwise Integration with Respect to fBm""""Chapter 2: Parametric Estimation for Fractional Diffusion Processes""; ""2.1 Introduction""; ""2.2 SDEs and Local Asymptotic Normality""; ""2.3 Parameter Estimation for Linear SDEs""; ""2.4 Maximum Likelihood Estimation""; ""2.5 Bayes Estimation""; ""2.6 Berryâ€"Esseen-Type Bound for MLE""; ""2.7 ϵ-Upper and Lower Functions for MLE""; ""2.8 Instrumental Variable Estimation""; ""Chapter 3: Parametric Estimation for Fractional Ornsteinâ€"Uhlenbeck-Type Process""; ""3.1 Introduction""; ""3.2 Preliminaries""
  • 3.3 Maximum Likelihood Estimation3.4 Bayes Estimation
  • 3.5 Probabilities of Large Deviations of MLE and BE
  • 3.6 Minimum L1-Norm Estimation
  • Chapter 4: Sequential Inference for Some Processes Driven by fBm
  • 4.1 Introduction
  • 4.2 Sequential Maximum Likelihood Estimation
  • 4.3 Sequential Testing for Simple Hypothesis
  • Chapter 5: Nonparametric Inference for Processes Driven by fBm
  • 5.1 Introduction
  • 5.2 Identification for Linear Stochastic Systems
  • 5.3 Nonparametric Estimation of Trend
  • Chapter 6: Parametric Inference for some SDEs driven by processes related to fBm6.1 Introduction
  • 6.2 Estimation of the Translation of a Process Driven by fBm
  • 6.3 Parametric Inference for SDEs with Delay Governed by fBm
  • 6.4 Parametric Estimation for Linear System of SDEs driven by fBms with Different Hurst Indices
  • 6.5 Parametric Estimation for SDEs driven by Mixed fBm
  • 6.6 Alternate Approach for Estimation in Models driven by fBm
  • 6.7 Maximum Likelihood Estimation Under Misspecified Model
  • Chapter 7: Parametric estimation for processes driven by fractional Brownian sheet7.1 Introduction
  • 7.2 Parametric Estimation for Linear SDEs Driven by a Fractional Brownian Sheet
  • Chapter 8: Parametric Estimation for Processes Driven by Infinite-Dimensional fBm
  • 8.1 Introduction
  • 8.2 Parametric Estimation for SPDEs Driven by Infinite-Dimensional fBm
  • 8.3 Parametric Estimation for Stochastic Parabolic Equations Driven by Infinite-Dimensional fBm
  • Chapter 9: Estimation of Self-Similarity Index
  • 9.1 Introduction

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