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Decomposition of Nonlinear Stochastic Differential Systems

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Abstract

Decomposition of a system, i.e., representation of a system as a set of subsystems of lesser dimension, for a multivariate dynamic system described by a nonlinear Ito stochastic differential equation is investigated. The existence and explicit construction of coordinate systems (substitutions of variables) for decomposition are examined. Group-theoretic analysis of ordinary differential equations, which is effective for analyzing deterministic control systems, is also useful in studying the decomposition of stochastic systems. A relationship between the decompositions of the Ito stochastic system and its associated deterministic control system is determined. Examples are given.

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Shaikin, M.E., Shin, V.I. Decomposition of Nonlinear Stochastic Differential Systems. Automation and Remote Control 62, 409–421 (2001). https://doi.org/10.1023/A:1002806227638

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