This article is cited in 1 paper

Processing of Experimental Data

Integral representations of solutions for linear stochastic equations with multiplicative perturbances

M. E. Shaikin

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider the problem of explicitly representing the solutions of multiplicatively perturbed stochastic equations. We represent the solution as an integral Cauchy formula whose transition matrix is random in the case of multiplicative perturbations. Similar to deterministic theory, the transition matrix can be expressed in terms of the fundamental matrix or given by a stochastic Peano series. We give equations for statistical moments of the state vector and explicit integral representations of their solutions. For computing transition matrices of equations on moments, we use some group-theoretical notions and results whose usefulness is illustrated with simple examples.

Presented by the member of Editorial Board: A. I. Kibzun

Received: 02.03.2009

 English version: Automation and Remote Control, 2010, 71:4, 555–571

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