有界时滞非线性随机微分方程解的振动性和非振性

Non-oscillation and Oscillation in Solutions of Nonlinear Stochastic Differential Equations with Bounded Delay

研究了一类非线性随机时滞微分方程解的振动性和非振性,其中设定时滞可变且有界.依据该方程漂移项和扩散项的性质,证明了通过选定适当的初值,方程依概率存在正解;同时,给出了方程解几乎必然振动的一个充分条件.

This paper studies non-oscillation and oscillation in solutions of a nonlinear stochastic delay differential equation,in which the delay is time varying and bounded.Depending on the properties of the drift and the diffusion of the equation,positive solutions may exist with positive probability for suitable selected initial process,and a sufficient condition for the almost sure oscillation of the solutions is also established.