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moment equations of Linear It Stochastic Systems with Applications

Journal of Systems Engineering and Electronics 1998年第2期9卷 1-7页

作者： Deng Feiqi Liu Hongwei Feng Zhaoshu & Liu Yongqing(Department of Automatic Control Engineering, South China University of Technology,Guangzhou 510641, P. R. China)

In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Ito stochastic systems is *** the time-invariant stochastic systems,the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Ito stochastic systems.

关键词： moment equations Mean-square stability Necessary and sufficient condition Algorithm

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Laplace-Transform Finite Element Solution of Nonlocal and Localized Stochastic moment equations of Transport

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Communications in Computational Physics 2009年第6期6卷 131-161页

作者： Eric Morales-Casique Shlomo P.Neuman Department of Hydrology and Water Resources University of ArizonaTucsonArizona 85721USA

Morales-Casique et al.(*** Res.,29(2006),pp.1238-1255)developed exact first and second nonlocal moment equations for advective-dispersive transport in finite,randomly heterogeneous geologic *** velocity and concentration in these equations are generally nonstationary due to trends in heterogeneity,conditioning on site data and the influence of forcing ***-Casique et al.(*** Res.,29(2006),pp.1399-1418)solved the Laplace transformed versions of these equations recursively to second order in the standard deviationσY of(natural)log hydraulic conductivity,and iteratively to higher-order,by finite elements followed by numerical inversion of the Laplace *** did the same for a space-localized version of the mean transport *** we recount briefly their theory and algorithms;compare the numerical performance of the Laplace-transform finite element scheme with that of a high-accuracy ULTIMATE-QUICKEST algorithm coupled with an alternating split operator approach;and review some computational results due to Morales-Casique et al.(*** Res.,29(2006),pp.1399-1418)to shed light on the accuracy and computational efficiency of their recursive and iterative solutions in comparison to conditional Monte Carlo simulations in two spatial dimensions.

关键词： Geologic media porous media random heterogeneity conditioning stochastic transport moment equations nonlocality localization Laplace transform finite elements ultimatequickest

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Stability of a delayed predator prey model in a random environment

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Chinese Physics B 2015年第11期24卷 140-145页

作者：靳艳飞谢文贤 Department of Mechanics Beijing Institute of Technology Department of Applied Mathematics Northwestern Polytechnical University

The stability of the first-order and second-order solution moments for a Harrison-type predator-prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Ito interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.

关键词： delay-independent stability predator-prey model moment equations environmental noise

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