Fractional Processes: from Poisson to Branching One

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and L`evy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distributions of the normalized variable Z = N/ N are found for both processes.

• Type: Journal
• Year: 2008
• Where: IJBC
• Authors: V. V. Uchaikin, D. O. Cahoy, R. T. Sibatov
• Keywords: Fractional Generalizations, IJBC 2006, IJBC 2008, L`evy Stable Densities, Monte Carlo Algorithm