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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Properties of solutions of stochastic differential equations with random coefficients, non-Lipschitzian diffusion, and Poisson measures


Author: V. P. Zubchenko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 11-26
MSC (2010): Primary 60H10; Secondary 60H05, 60J65
Published electronically: August 2, 2011
MathSciNet review: 2790480
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Abstract: The existence and uniqueness of a solution of a stochastic differential equation with random coefficients, non-Lipschitzian diffusion, and with centered as well as with non-centered Poisson measures are proved. We estimate the probability that a solution eventually becomes negative. We find conditions for the existence of a nonnegative solution.


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Additional Information

V. P. Zubchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: v_zubchenko@ukr.net

DOI: http://dx.doi.org/10.1090/S0094-9000-2011-00824-1
PII: S 0094-9000(2011)00824-1
Keywords: Stochastic differential equations, non-Lipschitzian diffusion, Poisson measure, existence and uniqueness of a solution, nonnegativity of a solution, ruin probability
Received by editor(s): July 10, 2009
Published electronically: August 2, 2011
Additional Notes: The author is indebted to the European Commission for their support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2011 American Mathematical Society