The Annals of Applied Probability

Abstract nonlinear filtering theory in the presence of fractional Brownian motion

L. Coutin and L. Decreusefond

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Abstract

We develop the filtering theory in the case where both the signal and the observation are solutions of some stochastic differential equation driven by a multidimensional fractional Brownian motion. We show that the classical approach fails to give a closed equation for the filter and we develop another approach using an auxiliary process-valued semimartingale which solves this problem theoretically.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 4 (1999), 1058-1090.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962865

Digital Object Identifier
doi:10.1214/aoap/1029962865

Mathematical Reviews number (MathSciNet)
MR1728555

Zentralblatt MATH identifier
0956.60058

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations

Keywords
Filtering theory fractional Brownian motion Malliavin calculus stochastic differential equation

Citation

Coutin, L.; Decreusefond, L. Abstract nonlinear filtering theory in the presence of fractional Brownian motion. Ann. Appl. Probab. 9 (1999), no. 4, 1058--1090. doi:10.1214/aoap/1029962865. https://projecteuclid.org/euclid.aoap/1029962865


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