Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, November 1, 2010

Schreiber 006, 12:15

Iddo Eliazar

Holon Institute of Technology, Israel

Universal generation of fractal statistics

Abstract: We present a stochastic superposition model which is capable of generating – in a universal fashion – various “fractal statistics”: anomalous diffusion, Levy laws, 1/f noises, and self-similarity. The model considers the superposition of independent stochastic processes: all processes sharing a common – yet arbitrary – stochastic process-pattern; each process having its own random parameters – initiation epoch, amplitude, and frequency. The stochastic superposition model is general and robust, and arises naturally in diverse fields of Science and Engineering: transmission channels and routers, and Internet servers in Communication; background noises in Physics and Electrical Engineering; probe dynamics in “stochastic baths”, and shot noise processes in Physics; river flows in Hydrology; tax revenues of states in Economics. Considering a specific process-statistic of the superposition model’s output, we focus on the following universality question: Is there a randomization of the processes’ parameters which renders the output’s process-statistic invariant with respect to the processes’ common stochastic pattern? The answer – for various process-statistics – turns out to be affirmative, and yields the aforementioned “fractal statistics”. This research thus establishes a unified framework that: (i) explains the universal emergence of “fractal statistics” in diverse fields of Science and Engineering, and (ii) provides an explicit model and randomization-algorithms that universally yield desired “fractal statistics”. The talk does not assume prior knowledge of stochastic processes.

Joint work with Joseph Klafter, Tel Aviv University.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006