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A cumulant expansion for stochastic linear differential equations. II

Authors
Journal
Physica
0031-8914
Publisher
Elsevier
Publication Date
Volume
74
Issue
2
Identifiers
DOI: 10.1016/0031-8914(74)90122-0
Disciplines
  • Mathematics

Abstract

Abstract The differential equation that was derived in Part I for the average of a solution of a linear stochastic differential equation is here rederived in a more formal manner. It is possible to construct all terms of the expansion. Each term is an integral over an “ordered cumulant”, which is a certain combination of moments of the random coefficients. The ordered cumulants are obtained from the familiar cumulants by writing all factors in a prescribed order. A summary of the result is given in Sec. 5.

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