Asymptotic behavior of solutions of linear stochastic differential systems
HTML articles powered by AMS MathViewer
- by Avner Friedman and Mark A. Pinsky PDF
- Trans. Amer. Math. Soc. 181 (1973), 1-22 Request permission
Abstract:
Following Kasminski, we investigate asymptotic behavior of solutions of linear time-independent Itô equations. We first give a sufficient condition for asymptotic stability of the zero solution. Then in dimension 2 we determine conditions for spiraling at a linear rate. Finally we give applications to the Cauchy problem for the associated parabolic equation by the use of a tauberian theorem.References
- M. I. Freĭdlin, The exterior Dirichlet problem for the class of bounded functions, Teor. Verojatnost. i Primenen 11 (1966), 463–471 (Russian, with English summary). MR 0201812
- Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
- Avner Friedman, Limit behavior of solutions of stochastic differential equations, Trans. Amer. Math. Soc. 170 (1972), 359–384. MR 378118, DOI 10.1090/S0002-9947-1972-0378118-9
- I. I. Gihman and A. V. Skorohod, Stokhasticheskie differentsial′nye uravneniya, Izdat. “Naukova Dumka”, Kiev, 1968 (Russian). MR 0263172
- R. Z. Has′minskiĭ, Necessary and sufficient conditions for asymptotic stability of linear stochastic systems, Teor. Verojatnost. i Primenen. 12 (1967), 167–172 (Russian, with English summary). MR 0211465
- F. Kozin and S. Prodromou, Necessary and sufficient conditions for almost sure sample stability of linear Ito equations, SIAM J. Appl. Math. 21 (1971), 413–424. MR 305479, DOI 10.1137/0121044
- H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
- H. R. Pitt, Tauberian theorems, Tata Institute of Fundamental Research, Monographs on Mathematics and Physics, vol. 2, Oxford University Press, London, 1958. MR 0106376
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 181 (1973), 1-22
- MSC: Primary 60H10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0319268-3
- MathSciNet review: 0319268