本文研究生成元f关于(y,z)线性增长,关于y左连续和左Lipschitz且关于z连续的一维倒向重随机微分方程,证明其最小解的存在性,得到其最小解的一个比较定理,推广了几个已有结果.
In this paper, we first prove that a one-dimensional backward doubly stochastic differential equation admits a minimal solution when the generator f is left-continuous and left-Lipschtiz in y, and continuous in z and of linear growth in (y, z). Then, we establish a comparison theorem under the above assumptions. Our results improve some existing works.