AI 中文总结
本文针对连续观测量子系统中扩散随机主方程的参数估计问题，提出基于确定性平均态的最大对比估计量，并证明其强相合性与渐近正态性，同时给出可计算的相合协方差估计量以评估不确定性。
AI 中文摘要
对量子系统的连续测量会产生条件量子态的随机动力学，该动力学由扩散随机主方程描述。本文研究了当哈密顿量和测量算符依赖于未知参数时此类方程的参数估计问题。基于具有已知初始状态的多个独立观测轨迹，我们利用确定性平均态构造了一个对比函数，并为未知参数定义了最大对比估计量。我们证明了在固定时间、多轨迹渐近机制下参数估计量的强相合性和渐近正态性。关键在于渐近正态性中出现的协方差矩阵具有一种自然导致相合协方差估计量的形式。该协方差估计量可由观测数据连同确定性平均动力学计算得出，因此渐近正态性结果可用于构造标准误差并评估参数估计量的不确定性。
英文摘要
Continuous measurement of quantum systems gives rise to stochastic dynamics of the conditional quantum state, described by diffusive stochastic master equations. In this paper, we study parameter estimation for such equations when the Hamiltonian and measurement operators depend on unknown parameters. Based on multiple independent observed trajectories with a known initial state, we construct a contrast function using the deterministic averaged state and define a maximum contrast estimator for the unknown parameter. We prove strong consistency and asymptotic normality of the parameter estimator in a fixed-time, many-trajectory asymptotic regime. A key point is that the covariance matrix appearing in the asymptotic normality is given in a form that naturally leads to a consistent covariance estimator. This covariance estimator is computable from the observed data together with the deterministic averaged dynamics, so the asymptotic normality result can be used to construct standard errors and assess uncertainty for the parameter estimator.
Comments27 pages, 2 figures
