Some methods of stochastic calculus for fractional Brownian motion

Author

Duncan, T.E. ; Hu, Y.Z. ; Pasik-Duncan, B.

Author_Institution

Dept. of Math., Kansas Univ., Lawrence, KS, USA

Volume

3

fYear

1999

fDate

1999

Firstpage

2390

Abstract

Some results for stochastic calculus for a fractional Brownian motion are described and an application to identification is given. A stochastic integral is defined that has mean zero and an explicit expression is given for the second moment. Another stochastic integral is defined and the two stochastic integrals are explicitly related. An Ito formula is given for a smooth function of a fractional Brownian motion. A parameter identification problem is described for a linear stochastic differential equation with fractional Brownian motion and a family of strongly consistent estimates is given

Keywords

Brownian motion; integral equations; parameter estimation; Ito formula; fractional Brownian motion; linear stochastic differential equation; parameter identification problem; second moment; smooth function; stochastic calculus; stochastic integral; strongly consistent estimates; Brownian motion; Calculus; Differential equations; Mathematics; Motion estimation; Parameter estimation; Reservoirs; Stochastic processes; Stochastic resonance; Water resources;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1999. Proceedings of the 38th IEEE Conference on

Conference_Location

Phoenix, AZ

ISSN

0191-2216

Print_ISBN

0-7803-5250-5

Type

conf

DOI

10.1109/CDC.1999.831282

Filename

831282