Existence and uniqueness of solutions of stochastic differential equations with non-Lipschitz diffusion and Poisson measure
Authors:
V. P. Zubchenko and Yu. S. Mishura
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 80 (2010), 47-59
MSC (2000):
Primary 60H10; Secondary 60H05, 60J65
DOI:
https://doi.org/10.1090/S0094-9000-2010-00793-9
Published electronically:
August 18, 2010
MathSciNet review:
2541951
Full-text PDF Free Access
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Abstract: The existence and uniqueness of a solution of a stochastic differential equation with a non-Lipschitz diffusion for cases of both centered and non-centered Poisson measures is proved. We prove that the pathwise uniqueness of a solution and the existence of a weak solution imply the existence of a strong solution for such equations.
References
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References
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Additional Information
V. P. Zubchenko
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
v_zubchenko@ukr.net
Yu. S. Mishura
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue, 2, Kiev 03127, Ukraine
Email:
myus@univ.kiev.ua
Keywords:
Stochastic differential equation,
non-Lipschitz diffusion,
Poisson measure,
weak solution,
existence and uniqueness of solution
Received by editor(s):
February 25, 2009
Published electronically:
August 18, 2010
Additional Notes:
The authors are grateful to the European Commission for support of their investigations in the framework of the Program “Marie Curie Actions”, grant “Multifractionality” PIRSES-GA-2008-230804
Article copyright:
© Copyright 2010
American Mathematical Society
