Longest excursion of fractional Brownian motion: numerical evidence of non-Markovian effects.
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<H<1. We show that in the large t limit, <l(max)(t)> proportional to variantQ(infinity)t, where Q(infinity) identical with Q(infinity)(H) depends continuously on H. These results are compared with exact analytical results for a renewal process with an associated persistence exponent theta=1-H. This comparison shows that Q(infinity)(H) carries the clear signature of non-Markovian effects for H not equal 1/2. The preasymptotic behavior of <l(max)(t)> is also discussed.
García-García
Reinaldo
R
Centro Atómico Bariloche, 8400 S. C. de Bariloche, Argentina.
Rosso
Alberto
A
Schehr
Grégory
G