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Theory of Probability and Mathematical Statistics

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Comparison theorem for solutions of parabolic stochastic equations with an absorber


Author: S. A. Mel’nik
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 161-173
MSC (2010): Primary 60F10; Secondary 62F05
DOI: https://doi.org/10.1090/tpms/957
Published electronically: August 10, 2015
MathSciNet review: 3242028
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Abstract: A comparison theorem is proved for solutions of the Cauchy problem for a quasi-linear parabolic stochastic equation. The drift and diffusion coefficients of this equation do not necessarily satisfy the Lipschitz condition. The drift coefficient is assumed to be an absorber.


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Additional Information

S. A. Mel’nik
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute for Applied Mathematics and Mechanics, National Academy of Science of Ukraine, R. Luxembyrg Street, 74, Donetsk, 83114, Ukraine
Email: s.a.melnik@yandex.ua

DOI: https://doi.org/10.1090/tpms/957
Keywords: Stochastic partial differential equation, comparison theorem
Received by editor(s): November 23, 2012
Published electronically: August 10, 2015
Additional Notes: This research was partially supported by the State Foundation for Fundamental Researches of Ukraine and RFFI (Russian Federation), grant $Φ$40.1/023
Article copyright: © Copyright 2015 American Mathematical Society