Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.

@article{Delorme2015MaximumOA,
  title={Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory.},
  author={Mathieu Delorme and Kay Joerg Wiese},
  journal={Physical review letters},
  year={2015},
  volume={115 21},
  pages={210601}
}
Fractional Brownian motion is a non-Markovian Gaussian process X_{t}, indexed by the Hurst exponent H. It generalizes standard Brownian motion (corresponding to H=1/2). We study the probability distribution of the maximum m of the process and the time t_{max} at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting H=1/2+ϵ. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical… CONTINUE READING
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