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Process with delta-correlated cumulants

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  • 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
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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.
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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

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