Fractional Brownian Motion and the Markov Property

  title={Fractional Brownian Motion and the Markov Property},
  author={Laure Coutin},
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear func-tionals of an infinite dimensional Markov process. This leads nat-uraly to : • An efficient algorithm to approximate the process. • An ergodic theorem which applies to functionals of the type t 0 φ(V h (s)) ds where V h (s) = t 0 h(t − u) dB u . 


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Testing for a change of the longmemory parameter

G. Montseny J. Audounet
Biometrika • 1993

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