CAJ | 학술논문

　　旨在研究非Lipschitz条件下Ch -空间中具有无穷时滞的中立型随机泛函微分方程的解对初值的连续依赖性。 Ch-空间不同于一般的有界连续函数空间，即BC空间；而无穷时滞的随机泛函微分方程的研究方法亦区别于有限时滞的随机泛函微分方程。因此，利用了Bihari不等式及其推论来进行稳定性的推导，结合Jensen不等式、Cauchy不等式等重要的不等式，得到了在本文的假设条件下，方程的解是均方稳定的这一结果。由此可见，在一定的条件下，将空间进行推广变化后，具有无穷时滞的中立型随机泛函微分方程仍然具备一些很好的性质。
　　지재연구비Lipschitz조건하Ch -공간중구유무궁시체적중립형수궤범함미분방정적해대초치적련속의뢰성。 Ch-공간불동우일반적유계련속함수공간，즉BC공간；이무궁시체적수궤범함미분방정적연구방법역구별우유한시체적수궤범함미분방정。인차，이용료Bihari불등식급기추론래진행은정성적추도，결합Jensen불등식、Cauchy불등식등중요적불등식，득도료재본문적가설조건하，방정적해시균방은정적저일결과。유차가견，재일정적조건하，장공간진행추엄변화후，구유무궁시체적중립형수궤범함미분방정잉연구비일사흔호적성질。
The purpose of this paper is to study the stability of the solution to neutral stochastic functional differ -ential equations with infinite delay at phase space Ch under non-Lipschitz conditions on the coefficients .Phase space Ch is different from generally boundary continuous function space , which is called phase space BC;where-as, the research method of stochastic functional differential equations with infinite delay is also distinguished from stochastic functional differential equations with finite delay .In this paper, we deduce the stability by means of Bihari inequality and its corollary , Jensen inequality,Cauchy inequality and other important inequalities .Final-ly, we obtain stability in mean square of the solution to INSFDEs under the assumptions of this paper .Thus it can be seen that under certain conditions , after the generalization of the phase space , neutral stochastic function-al differential equations with infinite delay still possesses its good qualities .