IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v117y1983i1p212-226.html
   My bibliography  Save this article

Systems under the influence of white and colored poisson noise

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437183900316
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(83)90031-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roerdink, J.B.T.M, 1982. "A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 557-587.
    2. Roerdink, J.B.T.M., 1981. "Inhomogeneous linear random differential equations with mutual correlations between multiplicative, additive and initial-value terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(1), pages 23-57.
    3. Lindenberg, Katja & West, Bruce J., 1984. "Finite correlation time effects in nonequilibrium phase transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 25-47.
    4. Kondepudi, D.K. & Nelson, G.W., 1984. "Chiral-symmetry-breaking states and their sensitivity in nonequilibrium chemical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 465-496.
    5. Chechetkin, V.R. & Lutovinov, V.S. & Samokhin, A.A., 1991. "On the diffusion of passive impurities in random flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 175(1), pages 87-113.
    6. Stewart, Glen R., 1982. "Long-time behavior of a non-Markovian Brownian oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(3), pages 519-530.
    7. van Kampen, N.G., 1980. "Process with delta-correlated cumulants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 489-495.
    8. Gang, Hu, 1985. "Master equation without strict detailed balance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 132(2), pages 586-592.
    9. Henery, R.J., 1982. "The short-time evolution of a non-linear oscillator driven by white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 321-330.
    10. Gorini, Vittorio & Verri, Maurizio & Frigerio, Alberto, 1989. "Non-markovian behavior in low-temperature damping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 161(2), pages 357-384.
    11. Dekker, H., 1980. "On the path integral for diffusion in curved spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(3), pages 586-596.
    12. Shapiro, V.E. & Loginov, V.M., 1978. "“Formulae of differentiation” and their use for solving stochastic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 563-574.
    13. Kagermann, H., 1982. "Stochastic equations arising from test particle problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(1), pages 199-206.
    14. Brey, J.J. & Casado, J.M. & Morillo, M., 1984. "Renormalized equations for a weakly nonlinear Duffing oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 481-496.
    15. Dekker, H., 1991. "Multisite spin hopping analysis of multilevel dissipative quantum tunneling and coherence at finite temperatures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(2), pages 289-331.
    16. Dekker, H., 1980. "Critical dynamics the expansion of the master equation including a critical point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 55-79.
    17. Wulbrand, Wilhelm & Kagermann, Henning, 1985. "The influence of random temperature modulation on the convective instability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 131(1), pages 182-196.
    18. Das, Amal K., 1979. "Stochastic diffusion in a periodic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(3), pages 528-544.
    19. Möbius, A. & Vojta, G., 1978. "Statistical theory of electron transport in open electron-phonon systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 94(2), pages 321-338.
    20. Marshall, T.W., 1980. "Brownian motion and quasi-Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 172-182.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:212-226. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.