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Systems under the influence of white and colored poisson noise

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  • Barcons, F.X.
  • Garrido, L.

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.

Suggested Citation

  • Barcons, F.X. & Garrido, L., 1983. "Systems under the influence of white and colored poisson noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 212-226.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:212-226
    DOI: 10.1016/0378-4371(83)90031-6
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    References listed on IDEAS

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    1. West, Bruce J. & Lindenberg, Katja & Seshadri, V., 1980. "Brownian motion of harmonic systems with fluctuating parameters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 470-488.
    2. Rodríguez, R.F. & Van Kampen, N.G., 1976. "Systematic treatment of fluctuations in a nonlinear oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 347-362.
    3. David M. Lefever, 1979. "Survey of time and savings deposits at commercial banks, January 1979," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue May, pages 387-392.
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