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ISSN 1547-7363(online) ISSN 0094-9000(print)
Properties of solutions of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion
Authors:
Yu. S. Mishura, S. V. Posashkova and G. M. Shevchenko
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 79 (2009), 117-126
MSC (2000):
Primary 60H10; Secondary 91B28
DOI:
https://doi.org/10.1090/S0094-9000-09-00774-1
Published electronically:
December 28, 2009
MathSciNet review:
2494541
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Properties of solutions of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion are studied in the paper. Conditions on the coefficients of an equation are obtained ensuring that a solution does not vanish over a finite time interval in the case of the diffusion $\sigma (t)\sqrt {x}$. We prove a limit theorem that solutions continuously depend on the parameter $n$ in the space $L_1(\mathsf {P})$ for a sequence of stochastic differential equations with nonhomogeneous coefficients and non-Lipschitz diffusion.
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Additional Information
Yu. S. Mishura
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
myus@univ.kiev.ua
S. V. Posashkova
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
revan1988@gmail.com
G. M. Shevchenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
zhora@univ.kiev.ua
Keywords:
Stochastic differential equations,
non-Lipschitz diffusion,
Cox–Ingersoll–Ross model,
continuous dependence on a parameter
Received by editor(s):
March 12, 2008
Published electronically:
December 28, 2009
Article copyright:
© Copyright 2009
American Mathematical Society