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http://bura.brunel.ac.uk/handle/2438/419
Title: | Growing random sequences |
Authors: | Krasikov, I Rodgers, GJ Tripp, CE |
Keywords: | Statistical moment;Random sequences;Power law;Exact solution;Probability;Probability distribution |
Issue Date: | 2004 |
Publisher: | Institute of Physics Publishing |
Citation: | Journal of Physics A: Mathematical and General, 37(6): 2365-2370(6), Feb 2004 |
Abstract: | We consider the random sequence x[n] = x[n-1] + 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 non-random sequence P[n](q) = δ[q,β(n-1)]. |
URI: | http://www.iop.org/EJ/journal/JPhysA/8 http://bura.brunel.ac.uk/handle/2438/419 |
DOI: | http://dx.doi.org/10.1088/0305-4470/37/6/026 |
Appears in Collections: | Mathematical Physics Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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Growing Random Sequences.pdf | 337.76 kB | Adobe PDF | View/Open |
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