论文信息 - Parametrically stochastic linear differential equations

Parametrically stochastic linear differential equations

In this paper we study the asymptotic properties of a family of Ito equations. Various equestions about the existence and uniqueness of invariant measures are resolved by using properties of the moments. In particular, the determinateness of the moment problem is related to a certain compactness condition of a Lie algebra associated with the infinitesimal generator of the process.

Roger W. Brockett | R. Brockett

[1] David L. Elliott,et al. Diffusions on Manifolds Arising from Controllable Systems , 1973 .

[2] U. Haussmann. On the Existence of Moments of Stationary Linear Systems with Multiplicative Noise , 1974 .

[3] R. Brockett. Lie Algebras and Lie Groups in Control Theory , 1973 .

[4] W. Feller,et al. An Introduction to Probability Theory and Its Application. , 1951 .

[5] R. Khas'minskii,et al. Stability of a linear system with random disturbances of its parameters , 1967 .

[6] U. Haussmann. Stability of Linear Systems with Control Dependent Noise , 1973 .

[7] J. L. Willems,et al. Stability of higher order moments for linear stochastic systems , 1975 .

[8] D. Mayne,et al. Geometric Methods in System Theory , 1973 .

[9] W. Wonham. Random differential equations in control theory , 1970 .

[10] R. Brockett. Lie Theory and Control Systems Defined on Spheres , 1973 .

[11] M. Zakai. A Lyapunov Criterion for the Existence of Stationary Probability Distributions for Systems Perturbed by Noise , 1969 .

[12] N. Akhiezer,et al. The Classical Moment Problem. , 1968 .

[13] U. G. Haussmann,et al. Optimal Stationary Control with State Control Dependent Noise , 1971 .

[14] D. Kleinman. On the stability of linear stochastic systems , 1969 .

[15] A. T. Bharucha-Reid,et al. Probabilistic methods in applied mathematics , 1968 .

[16] J. Willems,et al. Frequency domain stability criteria for stochastic systems , 1971 .