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Inhomogeneous linear random differential equations with mutual correlations between multiplicative, additive and initial-value terms

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  • Roerdink, J.B.T.M.

Abstract

The cumulant expansion for linear stochastic differential equations is extended to the general case in which the coefficient matrix, the inhomogeneous part and the initial condition are all random and, moreover, statistically interdependent. The expansion now involves not only the autocorrelation functions of the coefficient matrix (as in the homogeneous case) but also crosscorrelation functions of the coefficient matrix with the inhomogeneous part and with the initial value term. As a first illustration we consider an exactly solvable stochastic differential equation with initial correlations and compare the exact solution with that of the cumulant expansion. Secondly we show in general how the method can be used for the calculation of second moments, and treat the harmonic oscillator with random frequency and driving term as an example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:109:y:1981:i:1:p:23-57
    DOI: 10.1016/0378-4371(81)90037-6
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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.
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    3. van Kampen, N.G., 1980. "Process with delta-correlated cumulants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(3), pages 489-495.
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