Properties of solutions of stochastic differential equations with random coefficients, non-Lipschitzian diffusion, and Poisson measures
Author:
V. P. Zubchenko
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 82 (2011), 11-26
MSC (2010):
Primary 60H10; Secondary 60H05, 60J65
DOI:
https://doi.org/10.1090/S0094-9000-2011-00824-1
Published electronically:
August 2, 2011
MathSciNet review:
2790480
Full-text PDF Free Access
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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.
References
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References
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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
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
