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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Comparison theorem for solutions of parabolic stochastic equations with an absorber

S. A. Mel’nik

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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.

Keywords: Stochastic partial differential equation, comparison theorem

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