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Title:  Growing random sequences 
Authors:  Krasikov, I Rodgers, GJ Tripp, CE 
Keywords:  Statistical moment Random sequences Power law Exact solution Probability Probability distribution 
Publication Date:  2004 
Publisher:  Institute of Physics Publishing 
Citation:  Journal of Physics A: Mathematical and General, 37(6): 23652370(6), Feb 2004 
Abstract:  We consider the random sequence x[n] = x[n1] + yxq, with y > 0, where q = 0, 1,..., n  1 is chosen randomly from a probability distribution P[n] (q). When all q are chosen with equal probability, i.e. P[n](q) = 1/n, we obtain an exact solution for the mean <x[n]> and the divergence of the second moment <x[n]2> as functions of n and y. For y = 1 we examine the divergence of the mean value of x[n], as a function of n, for the random sequences generated by power law and exponential P[n](q) and for the nonrandom sequence P[n](q) = δ[q,β(n1)]. 
URI:  http://www.iop.org/EJ/journal/JPhysA/8 http://bura.brunel.ac.uk/handle/2438/419 
DOI:  http://dx.doi.org/10.1088/03054470/37/6/026 
Appears in Collections:  Mathematics School of Information Systems, Computing and Mathematics Research Papers Mathematical Physics

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