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Fractional processes: from Poisson to branching one. (English) Zbl 1157.60324

Summary: Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Lèvy stable densities are discussed and used for the 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 \(Z = N / \langle N \rangle\) are found for both processes.

MSC:

60G99 Stochastic processes
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