Generation and monitoring of discrete stable random processes using multiple immigration population models
| Autor: | E. Jakeman, J O Matthews, Keith I. Hopcraft |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
education.field_of_study
Series (mathematics) Stochastic process Population size Autocorrelation Population General Physics and Astronomy Statistical and Nonlinear Physics Population model Range (statistics) Econometrics Statistical physics education Mathematical Physics Mathematics Event (probability theory) |
| Zdroj: | Journal of Physics A: Mathematical and General. 36:11585-11603 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/36/46/004 |
| Popis: | Some properties of classical population processes that comprise births, deaths and multiple immigrations are investigated. The rates at which the immigrants arrive can be tailored to produce a population whose steady state fluctuations are described by a pre-selected distribution. Attention is focused on the class of distributions with a discrete stable law, which have power-law tails and whose moments and autocorrelation function do not exist. The separate problem of monitoring and characterizing the fluctuations is studied, analysing the statistics of individuals that leave the population. The fluctuations in the size of the population are transferred to the times between emigrants that form an intermittent time series of events. The emigrants are counted with a detector of finite dynamic range and response time. This is modelled through clipping the time series or saturating it at an arbitrary but finite level, whereupon its moments and correlation properties become finite. Distributions for the time to the first counted event and for the time between events exhibit power-law regimes that are characteristic of the fluctuations in population size. The processes provide analytical models with which properties of complex discrete random phenomena can be explored, and in addition provide generic means by which random time series encompassing a wide range of intermittent and other discrete random behaviour may be generated. |
| Databáze: | OpenAIRE |
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