|
Avtomatika i Telemekhanika, 2010, Issue 4, Pages 16–33
(Mi at801)
|
|
|
|
This article is cited in 1 scientific paper (total 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.
Citation:
M. E. Shaikin, “Integral representations of solutions for linear stochastic equations with multiplicative perturbances”, Avtomat. i Telemekh., 2010, no. 4, 16–33; Autom. Remote Control, 71:4 (2010), 555–571
Linking options:
https://www.mathnet.ru/eng/at801 https://www.mathnet.ru/eng/at/y2010/i4/p16
|
|