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A comparison theorem for solutions of stochastic differential equations and its applications


Author: Zhi Yuan Huang
Journal: Proc. Amer. Math. Soc. 91 (1984), 611-617
MSC: Primary 60H10; Secondary 34F05
MathSciNet review: 746100
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Abstract: A new kind of comparison theorem in which an SDE is compared with two deterministic ODEs is established by means of the generalized sample solutions of SDEs. Using this theorem, we can compare solutions of two SDEs with different diffusion coefficients and obtain some asymptotic estimations for the paths of diffusion processes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746100-9
Keywords: Stochastic differential equation, comparison theorem, generalized sample solution, diffusion coefficient, Carathéodory conditions, explosion time, smooth approximation
Article copyright: © Copyright 1984 American Mathematical Society