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SUMMARY:Fractional diffusion of variable order and anomalous aggregation p
 henomenon - Mladen Savov (Sofia University St. Kliment Ohridski\, Bulgaria
 n Academy of Sciences)
DTSTART:20220225T100000Z
DTEND:20220225T103000Z
UID:TALK167843@talks.cam.ac.uk
DESCRIPTION:In this talk we consider a fractional diffusion of variable or
 der both in time and space which may be thought of as a particle moving in
  diverse porous milieu. Linking them to general semi-Markov processes we d
 iscuss the long-term behaviour of these diffusions when the derivative in 
 time is fractional of variable order and the spatial behaviour is Brownian
  motion. In particular depending on the variable order of the diffusion\, 
 we prove rigorously an anticipated anomalous behaviour\, that is the domin
 ation of the time the fractional diffusion spends in regions where the ord
 er of the diffusion is minimal compared to the time spent elsewhere. Under
  some conditions and depending on the variable order of the diffusion we a
 lso demonstrate that the probability to find the particle in regions where
  the order of the diffusion is minimal converges to one as time increases.
  The main techniques do not stem from the integro-differential equation so
 lved by the semigroup (in a mild sense) of these processes\, but depend on
  classical laws of the iterated logarithm for general Levy processes. This
  is a clear indication of interplay between the purely analytical and the 
 fluctuation approach.\n&nbsp\;\nThis is joint work with Bruno Toaldo (Tori
 no\, Italy)
LOCATION:Seminar Room 1\, Newton Institute
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