Abstract
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.
This paper was writeen while the author held a Guggenheim Fellowship, partial support from the U.S. Office of Naval Research under the Joint Services Electronics Program by Contract N00014-75-C-0648, Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass. is also acknowledged.
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© 1976 The Mathematical Programming Society
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Brockett, R.W. (1976). Parametrically stochastic linear differential equations. In: Wets, R.J.B. (eds) Stochastic Systems: Modeling, Identification and Optimization, I. Mathematical Programming Studies, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120760
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DOI: https://doi.org/10.1007/BFb0120760
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