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Theory of Probability and Mathematical Statistics

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Existence of a limit distribution of a solution of a linear inhomogeneous stochastic differential equation

Author: D. O. Ivanenko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 78 (2008).
Journal: Theor. Probability and Math. Statist. 78 (2009), 49-60
MSC (2000): Primary 60F05; Secondary 60J75
Published electronically: August 4, 2009
MathSciNet review: 2446848
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Abstract | References | Similar Articles | Additional Information

Abstract: We find conditions for the existence of a limit distribution (as $ t\rightarrow\infty$) of a vector process $ \xi$ defined in $ \mathbb{R}_+$ and determined by an inhomogeneous stochastic differential equation $ \xi(t)=\xi(0)-\xi\circ\alpha+f\ast\nu+g\ast\mu$, where $ \alpha$ is a nonrandom continuous increasing function, $ \nu$ and $ \mu$ are independent Poisson and centered Poisson measures, respectively.

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Additional Information

D. O. Ivanenko
Affiliation: Department of Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Keywords: Limit distribution, Poisson measure, It\^o's formula, Tauberian theorem
Received by editor(s): July 3, 2007
Published electronically: August 4, 2009
Article copyright: © Copyright 2009 American Mathematical Society

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