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- W2040809630 abstract "This paper concerns a representation of solutions and the stability of linear systems with multiplicative white noise, which is described by a vector Ito stochastic differential equation. The solution can be represented as a finite product of exponential matrices if Lie algebra generated by system matrices is solvable. If Lie algebra is not solvable, it is shown by the decomposition principle of Lie algebra that the problem of solving an equation can be reduced to the problem of solving a set of equations, whose corresponding Lie algebra is simple. Noting the structure of the sample solution, we present a technique of obtaining asymptotic stability conditions of sample solutions w.p.1, in the pth-order moment and in the pth-mean moment. The necessary and/or sufficient conditions of stability in some stochastic sense are obtained under certain conditions." @default.
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- W2040809630 date "1984-11-01" @default.
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- W2040809630 title "Decomposition and stability of linear systems with multiplicative noise" @default.
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- W2040809630 doi "https://doi.org/10.1016/0005-1098(84)90086-4" @default.
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