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SUMMARY: Arcsine law in fractional Brownian motion.
DTSTART;VALUE=DATE-TIME:20171121T103000Z
DTEND;VALUE=DATE-TIME:20171121T113000Z
DTSTAMP;VALUE=DATE-TIME:20180920T143719Z
UID:indico-event-6021@cern.ch
DESCRIPTION:The three arcsine laws are one of the most non-intuitive pedag
ogical properties of the Brownian motion. These deal with the following th
ree observables of a Brownian motion evolving in a finite time window: (1)
the fraction of time it remained positive\, (2) the last time it crossed
the origin\, (3) and the time when it reached its maximum. All three obser
vables have the same cumulative probability distribution expressed as an a
rcsine function\, hence the name arcsine law. I shall discuss how these th
ree laws change for a fractional Brownian motion which is a generalization
of the Brownian motion defined by Benoit Mandelbrot to describe anomalous
diffusion seen in many natural examples. This is a non-Markovian Gaussian
process indexed by Hurst exponent H (H=1/2 corresponds to the standard Br
ownian). Due to the non-Markovian nature analytical results are hard to ob
tain. I shall derive the three probability distributions and show that the
y are all different for general H.\n\nhttps://indico.tifr.res.in/indico/co
nferenceDisplay.py?confId=6021
LOCATION: AG 69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6021
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