Abstract
In this paper we employ Lyapunov-like function to establish some new comparison theorems for stochastic differential equations with different diffusion terms. Lyapunov-like function serves as a vehicle to transform a given complicated stochastic differential system into a relatively simpler system and therefore it is enough to investigate the properties of this simpler stochastic differential system. Our results generalize those of O'Brien [7] and Gal'cuk and Davis [5]. It is new to apply Lyapunov-like function to study the comparison theorems within the context of stochastic differential equations
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