IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v102y1980i3p489-495.html
   My bibliography  Save this article

Process with delta-correlated cumulants

Author

Listed:
  • van Kampen, N.G.

Abstract

In a recent paper1) a differential equation was studied which involves a stochastic process having the property that all its cumulants are delta-correlated. It is here shown that such processes consist of a random sequence of delta functions with random coefficients. As a consequence the solutions of the differential equation are Markov processes, whose master equation can be constructed. From it closed equations for the successive moments may be obtained, and the auto-correlation is determined, in agreement with the results of reference 1. Some generalizations are given in Appendices B and C.

Suggested Citation

  • van Kampen, N.G., 1980. "Process with delta-correlated cumulants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 489-495.
  • Handle: RePEc:eee:phsmap:v:102:y:1980:i:3:p:489-495
    DOI: 10.1016/0378-4371(90)90178-U
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719090178U
    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(90)90178-U?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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Javier Vitela, E. & Coronado, Manuel, 1989. "Non-equilibrium fluctuations of a Rayleigh particle in a two-component gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(3), pages 1180-1194.
    3. Dekker, H., 1986. "Escape over a potential barrier: The activation rate in bistable systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(1), pages 80-104.
    4. 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.
    5. Sibani, P. & van Kampen, N.G., 1983. "An exactly soluble relaxation problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 397-412.
    6. Buyevich, Yu.A. & Fedotov, S.P. & Tret'yakov, M.V., 1993. "Heterogeneous reaction affected by external noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 198(3), pages 354-367.

    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. 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.
    2. 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.
    3. Wissel, Christian, 1984. "Solution of the master equation of a bistable reaction system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(1), pages 150-163.
    4. 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.
    5. Schweitzer, Frank & Schimansky-Geier, Lutz & Ebeling, Werner & Ulbricht, Heinz, 1988. "A stochastic approach to nucleation in finite systems: Theory and computer simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 150(1), pages 261-279.
    6. 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.

    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:102:y:1980:i:3:p:489-495. 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.