This article is cited in 1 paper

Stochastic Systems

Resolvents of the Ito differential equations multiplicative with respect to the state vector

M. E. Shaikin

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

Abstract: Integral representations of solutions of linear multiplicatively perturbed differential equations are obtained, the diffusion part of which is bilinear on the state vector and the vector of independent Wiener processes. Equations of such class serve as models of stochastic systems with control functioning under conditions of parametric uncertainty or undesirable influence of external disturbances. The concepts and analytical apparatus of the theory of Lie algebras are used to find integral representations and fundamental matrices of the equations.

Keywords: multiplicative stochastic system, fundamental matrix, Fisk–Stratonovich differential, group-theoretic method, matrix Lie algebra, Wei–Norman theorem, stochastic resolvent.

Presented by the member of Editorial Board: A. V. Nazin

Received: 01.09.2022
Revised: 25.05.2023
Accepted: 09.06.2023

DOI: 10.31857/S0005231023080068

 English version: Automation and Remote Control, 2023, 84:8, 858–870