Asymptotic behavior of integral functionals of unstable solutions of one-dimensional Itô stochastic differential equations
Authors:
G. L. Kulinich, S. V. Kushnirenko and Y. S. Mishura
Journal:
Theor. Probability and Math. Statist. 89 (2014), 101-114
MSC (2010):
Primary 60H10
DOI:
https://doi.org/10.1090/S0094-9000-2015-00938-8
Published electronically:
January 26, 2015
MathSciNet review:
3235178
Full-text PDF Free Access
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Abstract: We consider one-dimensional stochastic differential equations with a homogeneous drift and unit diffusion. The drift is such that a unique strong solution is unstable. An explicit form of the normalizing factor is established for certain integral functionals of the unstable solution for which the weak convergence to a limiting process holds. As a result, we get a new class of limiting processes that are the functionals of Bessel diffusion processes.
References
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Additional Information
G. L. Kulinich
Affiliation:
Department of General Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, Kyiv, Ukraine, 01601
Email:
zag$_$mat@univ.kiev.ua
S. V. Kushnirenko
Affiliation:
Department of General Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 64/13, Volodymyrska Street, Kyiv, Ukraine, 01601
Email:
bksv@univ.kiev.ua
Y. S. Mishura
Affiliation:
Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 64/13 Volodymyrska Street, Kyiv, Ukraine, 01601
Email:
yumishura@gmail.com
Keywords:
Itô stochastic differential equation,
unstable solution,
asymptotic behavior of integral functionals
Received by editor(s):
December 12, 2012
Published electronically:
January 26, 2015
Article copyright:
© Copyright 2015
American Mathematical Society
