## Electronic Communications in Probability

### Fractional Brownian Motion and the Markov Property

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 3 (1998), paper no. 12, 95-107.

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

https://projecteuclid.org/euclid.ecp/1456935918

Digital Object Identifier
doi:10.1214/ECP.v3-998

Mathematical Reviews number (MathSciNet)
MR1658690

Zentralblatt MATH identifier
0921.60067

Rights

#### Citation

Carmona, Philippe; Coutin, Laure. Fractional Brownian Motion and the Markov Property. Electron. Commun. Probab. 3 (1998), paper no. 12, 95--107. doi:10.1214/ECP.v3-998. https://projecteuclid.org/euclid.ecp/1456935918

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