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

J.B.T.m Roerdink

Physica A: Statistical Mechanics and its Applications, 1982, vol. 112, issue 3, 557-587

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.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:112:y:1982:i:3:p:557-587

DOI: 10.1016/0378-4371(82)90196-0

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