Systems under the influence of white and colored poisson noise

F.X. Barcons and L. Garrido

Physica A: Statistical Mechanics and its Applications, 1983, vol. 117, issue 1, 212-226

Abstract: We deal in this paper with systems driven by white or colored Poisson noise. For a free Brownian particle under the influence of white Poisson noise an exact generalized master equation in position space is obtained. In the Gaussian and Smoluchowski limits, known results are recovered. For a general process defined by a stochastic differential equation, with colored Poisson noise, we find an approximate generalized master equation, including first order terms in the correlation time and the first correction to the gaussianity. Under a more restrictive approximation, the stationary distribution function is given. This is used to study the phase transition in the steady state for a Verhulst model. Corrections to the gaussianity are discussed in this case.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:117:y:1983:i:1:p:212-226

DOI: 10.1016/0378-4371(83)90031-6

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