Intertime jump statistics of state-dependent Poisson processes.
A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.
Daly
Edoardo
E
Department of Civil and Environmental Engineering and Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina 27708, USA. edaly@pratt.duke.edu
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Amilcare
A