中立型随机泛函微分方程解的存在唯一性(英文)

本文作者建立了中立型随机泛函微分方程解的一些基本理论.首先,利用不动点定理,作者在漂移系数和扩散系数仅满足连续的条件下研究了中立型随机泛函微分方程解的局部存在性,然后作者通过比较法建立了唯一性定理,并且在延拓定理的基础上给出了解的全局存在性.

Existence-uniqueness of the solutions for neutral stochastic functional differential equations

The main aim of this paper is to develop some basic theories of solutions of neutral stochastic functional differential equations (NSFDEs). Firstly, by fixed point theorem, the local existence of solutions for NSFDEs is studied under only the continuity condition for drift coefficient and diffusion coefficient. Secondly, a uniqueness theorem is established by comparison methods. Furthermore, the continuation theorem is obtained under which the global existence of solutions is presented for NSFDEs.