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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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal: Theor. Probability and Math. Statist. 80 (2010), 47-59
MSC (2000): Primary 60H10; Secondary 60H05, 60J65
Published electronically: August 18, 2010
MathSciNet review: 2541951
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Abstract | References | Similar Articles | Additional Information

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.


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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

DOI: https://doi.org/10.1090/S0094-9000-2010-00793-9
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