一类随机主方程的路径解
Pathwise Solution of a Class of Stochastic Master Equations
摘要：
在本文中，我们考虑了一类随机波和标量噪声的主方程，用于在量子光学建模开放系统和连续监测系统的替代制剂。通过应用J.M.C.从经典非线性滤波理论出发的克拉克路径重构技术。随机波和主方程的路径版本被定义为所有的驱动路径，并连续依赖于它们。在白噪声方程的情况下，我们推导出类似的克拉克的强大的近似。本文的结果对于实现量子系统的连续监测和测量反馈控制的滤波器，以及发展解开主方程的新型数值方法可能是有用的。通过一个例子说明了主要思想。
英文摘要：
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by applying J.M.C. Clark's pathwise reformulation technique from the theory of classical nonlinear filtering. The pathwise versions of the stochastic wave and master equations are defined for all driving paths and depend continuously on them. In the case of white noise equations, we derive analogs of Clark's robust approximations. The results in this paper may be useful for implementing filters for the continuous monitoring and measurement feedback control of quantum systems, and for developing new types of numerical methods for unravelling master equations. The main ideas are illustrated by an example.
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