The longest excursion of fractional Brownian motion : numerical evidence of non-Markovian effects
Reinaldo Garcia-Garcia 1, Alberto Rosso 2, Gregory Schehr 3 Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 81 (2010) 010102(R) We study, using exact numerical simulations, the statistics of the longest excursion l_{\max}(t) up to time t for the fractional Brownian motion with Hurst exponent 0 \propto Q_\infty t where Q_\infty \equiv Q_\infty(H) depends continuously on H, and in a […]