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A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations

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  • Roerdink, J.B.T.M

Abstract

It is shown that the cumulant expansion for linear stochastic differential equations, hitherto used to compute one-time averages of the solution process, is also capable of yielding the two-time correlation and probability density functions. The general case with a coefficient matrix, an inhomogeneous part and an initial condition which are all random and mutually correlated, is discussed. Two examples are given, the latter of which treats the harmonic oscillator with stochastic frequency and driving term studied before. Finally we investigate the relation of our method with the so-called smoothing method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:112:y:1982:i:3:p:557-587
    DOI: 10.1016/0378-4371(82)90196-0
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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.
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