奇异Itô随机系统几个重要基础问题的研究进展

近年来，一类由Itô随机微分方程驱动的奇异随机系统因其在实际领域中的广泛应用而备受关注.然而，系统方程同时包含奇异矩阵和扩散矩阵，大大增加了分析问题的复杂性.本文首先概述了奇异Itô随机系统几个重要基础问题的研究进展，主要包括:系统方程解的存在条件、广义Itô公式、容许性定义及稳定性问题.同时针对不同文献对上述问题的研究结果提出了自己的观点.最后对以上基础问题研究待解决的问题进行了展望.

Research advances of several important and basic problems for singular Itô stochastic systems

In recent years,singular stochastic systems governed by the Itô stochastic differential equation have received much attention due to their extensive applications to some practical areas.However,it is very complicated to discuss singular stochastic systems since the system equation includes both the singular matrix and the diffusion matrix simultaneously.In this paper,research development of several important and basic problems for singular Itô stochastic systems are concluded,including mainly the existence condition for the solution to the system equation,the general Itô formula,the definition of admissibility and the issue of stability.Also,some research perspectives are given for results of different references.Finally,some prospects to the unresolved problems are presented.