Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-03-25
Physics
Condensed Matter
Statistical Mechanics
13 pages, 8 figures
Scientific paper
We derive a functional equation for the mean first-passage time (MFPT) of a generic self-similar Markovian continuous process to a target in a one-dimensional domain and obtain its exact solution. We show that the obtained expression of the MFPT for continuous processes is actually different from the large system size limit of the MFPT for discrete jump processes allowing leapovers. In the case considered here, the asymptotic MFPT admits non-vanishing corrections, which we call residual MFPT. The case of L/'evy flights with diverging variance of jump lengths is investigated in detail, in particular, with respect to the associated leapover behaviour. We also show numerically that our results apply with good accuracy to fractional Brownian motion, despite its non-Markovian nature.
Benichou Olivier
Metzler Ralf
Tejedor Vincent
Voituriez Raphael
No associations
LandOfFree
Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-570996