Fractality in Physical Models: Probability Problems
Friday, September 28, 2001 - 9:30am - 10:30am
Gueorgui Moltchan (Russian Academy of Sciences)
We consider two objects: a simple sedimentation model in geology and the inviscid Burgers equation. In both of these cases we consider the problem of calculating fractal dimensions or multifractal characteristics of these physical objects. The problems are reduced to calculation of fine asymptotics for self-similar random processes, in particular, to the calculation of the probability nonexceedance of a fixed level for fractional Brownian motion (FBM or integrals of FBM) on a very long interval. Solved and unsolved problems will be discussed.