Generalized Arcsine Laws for Fractional Brownian Motion.

@article{Sadhu2018GeneralizedAL,
  title={Generalized Arcsine Laws for Fractional Brownian Motion.},
  author={T. Sadhu and Mathieu Delorme and K. J. Wiese},
  journal={Physical review letters},
  year={2018},
  volume={120 4},
  pages={
          040603
        }
}
The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus… Expand
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