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.
Information
Published: 1 January 2004
First available in Project Euclid: 28 November 2007
zbMATH: 1268.62101
MathSciNet: MR2126890
Digital Object Identifier: 10.1214/lnms/1196285383
Subjects:
Primary:
62M09
Secondary:
60G15
Keywords:
Bayes estimation
,
fractional Brownian motion
,
fractional Ornstein-Uhlenbeck type process
,
Girsanov-type theorem
,
linear stochastic systems
,
maximum likelihood estimation
,
nonparametric inference
,
self-similar process
Rights: Copyright © 2004, Institute of Mathematical Statistics
