Uchaikin, V. V.; Cahoy, D. O.; Sibatov, R. T. Fractional processes: from Poisson to branching one. (English) Zbl 1157.60324 Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 9, 2717-2725 (2008). 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. Cited in 30 Documents MSC: 60G99 Stochastic processes Keywords:fractional Poisson process; fractional Furry process; one-sided stable density PDFBibTeX XMLCite \textit{V. V. Uchaikin} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 9, 2717--2725 (2008; Zbl 1157.60324) Full Text: DOI arXiv References: [1] R. Botet and M. Ploszajczak, Universal Fluctuations: The Phenomenology of Hadronic Matter (World Scientific, Singapore, 2002) p. 369. · Zbl 1032.82015 · doi:10.1142/4916 [2] DOI: 10.1142/S0219477505002641 · doi:10.1142/S0219477505002641 [3] Dubkov A. A., Acta Phys. Polon. B 38 pp 1745– [4] Guy J., Chaos Solit. Fract. 12 pp 2577– [5] Harper W. R., Contact and Frictional Electrification (1967) [6] DOI: 10.1214/aop/1176996309 · Zbl 0323.60013 · doi:10.1214/aop/1176996309 [7] DOI: 10.1016/S1007-5704(03)00037-6 · Zbl 1025.35029 · doi:10.1016/S1007-5704(03)00037-6 [8] DOI: 10.1023/A:1004890226863 · doi:10.1023/A:1004890226863 [9] DOI: 10.1103/PhysRevB.12.2455 · doi:10.1103/PhysRevB.12.2455 [10] Shimizu K. T., Phys. Rev. B 63 pp 205316-1– [11] DOI: 10.1063/1.1661823 · doi:10.1063/1.1661823 [12] DOI: 10.1063/1.1661007 · doi:10.1063/1.1661007 [13] DOI: 10.1063/1.1661008 · doi:10.1063/1.1661008 [14] DOI: 10.1134/1.558905 · doi:10.1134/1.558905 [15] DOI: 10.1515/9783110935974 · Zbl 0944.60006 · doi:10.1515/9783110935974 [16] DOI: 10.1070/PU2003v046n08ABEH001324 · doi:10.1070/PU2003v046n08ABEH001324 [17] DOI: 10.1016/S0960-0779(02)00579-9 · Zbl 1042.60019 · doi:10.1016/S0960-0779(02)00579-9 [18] DOI: 10.1016/j.chaos.2005.05.019 · Zbl 1086.60022 · doi:10.1016/j.chaos.2005.05.019 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.