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1998 Fractional Brownian Motion and the Markov Property
Philippe Carmona, Laure Coutin
Author Affiliations +
Electron. Commun. Probab. 3: 95-107 (1998). DOI: 10.1214/ECP.v3-998

Abstract

Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to:

  • An efficient algorithm to approximate the process.

  • An ergodic theorem which applies to functionals of the type $$\int_0^t \phi(V_h(s)),ds \quad\text{where}\quad V_h(s)=\int_0^s h(s-u), dB_u,.$$

where $B$ is a real Brownian motion.

Citation

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Philippe Carmona. Laure Coutin. "Fractional Brownian Motion and the Markov Property." Electron. Commun. Probab. 3 95 - 107, 1998. https://doi.org/10.1214/ECP.v3-998

Information

Accepted: 27 October 1998; Published: 1998
First available in Project Euclid: 2 March 2016

zbMATH: 0921.60067
MathSciNet: MR1658690
Digital Object Identifier: 10.1214/ECP.v3-998

Subjects:
Primary: 60Fxx
Secondary: 26A33, 60A10, 60G15, 60J25, 65U05

JOURNAL ARTICLE
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