Title: Infinite Dimensional Mean-Field Belavkin Equation: Well-posedness and Derivation Show Chinese title

Title: 无限维平均场贝拉文金方程：适定性与推导

Abstract: We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described by Belavkin's filtering equation, we derive a mean-field approximation under minimal assumptions, extending prior results limited to bounded operators and finitedimensional settings. By establishing global well-posedness via fixed-point methods-avoiding measure-change techniques-we obtain higher regularity solutions. Furthermore, we prove rigorous convergence to the mean-field limit in an infinitedimensional framework. Our work provides the first derivation of such limits for wave functions in $L^2 (R^d)$, with implications for simulating and controlling large quantum systems. Show Chinese abstract

Abstract: 我们分析了在量子最优控制和平均场博弈中出现的随机薛定谔方程的平均场极限，其中N个相互作用的粒子经历连续的间接测量。 对于由贝拉夫金滤波方程描述的开放量子系统，我们在最小假设下推导出平均场近似，扩展了之前仅限于有界算子和有限维设置的结果。 通过建立全局适定性 via 不使用测度变换技术的不动点方法，我们得到了更高正则性的解。 此外，我们在无限维框架下证明了对平均场极限的严格收敛。 我们的工作首次推导了$L^2 (R^d)$中波函数的此类极限，对模拟和控制大型量子系统具有重要意义。