Self-similar processes, fractional Brownian motion and statistical inference



Institute of Mathematical Statistics Lecture Notes - Monograph Series

Self-similar processes, fractional Brownian motion and statistical inference

B. L. S. Prakasa Rao

Source: Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 98-125.

Abstract

Self-similar stochastic processes are used for stochastic modeling whenever it is expected that long range dependence may be present in the phenomenon under consideration. After discussing some basic concepts of self-similar processes and fractional Brownian motion, we review some recent work on parametric and nonparametric inference for estimation of parameters for linear systems of stochastic differential equations driven by a fractional Brownian motion.

Primary Subjects: 62M09
Secondary Subjects: 60G15
Keywords: self-similar process; fractional Brownian motion; fractional Ornstein-Uhlenbeck type process; Girsanov-type theorem; maximum likelihood estimation; Bayes estimation; nonparametric inference; linear stochastic systems

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196285383
Mathematical Reviews (MathSciNet): MR2126890

Digital Object Identifier: doi:10.1214/lnms/1196285383

2009 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series