Fractional Brownian Motion and the Markov Property

Philippe Carmona (Université Paul Sabatier)
Laure Coutin (Université Paul Sabatier)

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:
  1. An efficient algorithm to approximate the process.
  2. 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.

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Pages: 95-107

Publication Date: October 27, 1998

DOI: 10.1214/ECP.v3-998

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