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

DOI:
https://doi.org/10.1090/S0094-9000-09-00761-3

Published electronically:
August 4, 2009

MathSciNet review:
2446848

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We find conditions for the existence of a limit distribution (as ) of a vector process defined in and determined by an inhomogeneous stochastic differential equation , where is a nonrandom continuous increasing function, and 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

Email:
ida@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-09-00761-3

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