On the asymptotic degeneration of systems of linear inhomogeneous stochastic differential equations
Author:
Oleksander Il’chenko
Translated by:
S. Kvasko
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 76 (2007).
Journal:
Theor. Probability and Math. Statist. 76 (2008), 4148
MSC (2000):
Primary 60H10; Secondary 34F05
Published electronically:
July 10, 2008
MathSciNet review:
2368738
Fulltext PDF Free Access
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Abstract: Assuming the almost sure stability of a linear homogeneous system, we obtain sufficient conditions for the convergence to zero, in probability as well as pathwise, of solutions of the system of linear inhomogeneous stochastic differential equations.
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 I. I. Gikhman, A. V. Skorokhod, and M. I. Yadrenko, Probability Theory and Mathematical Statistics, ``Vyshcha Shkola'', Kyiv, 1979. (Russian)
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 A. V. Il'chenko, Stochastically bounded solutions of the linear inhomogeneous stochastic differential equation system, Theory Stoch. Process. 9(25) (2003), no. 12, 6572. MR 2080014 (2005h:60166)
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Additional Information
Oleksander Il’chenko
Affiliation:
Department of General Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
DOI:
http://dx.doi.org/10.1090/S0094900008007308
PII:
S 00949000(08)007308
Received by editor(s):
October 11, 2005
Published electronically:
July 10, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
