We establish the existence and some properties of viable solutions of lower semicontinuous quantum stochastic differential inclusions within the framework of the Hudson–Parthasarathy formulations of quantum stochastic calculus. The main results here are accomplished by establishing a major auxiliary selection result. The results here extend the classical Nagumo viability theorems,valid on finite dimensional Euclidean spaces, to the present infinite dimensional locally convex space of noncommutative stochastic processes.

中文翻译：

---

下半连续量子随机微分包含的可行解

我们在量子随机演算的哈德森-帕塔萨拉西公式的框架内，建立了下半连续量子随机微分包含物的可行解的存在性和某些性质。这里的主要结果是通过建立主要的辅助选择结果来实现的。这里的结果将在有限维欧几里得空间上有效的经典Nagumo生存定理扩展到了当前非交换随机过程的无穷局部凸空间。