发表机构
Huzhou Normal University（湖州师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为全耦合非线性均值场前向-后向随机差分方程建立有限时域可解性条件，通过支配-单调性方法证明唯一解，并用LQ缓冲调整模型验证定理及其开环优化器。
AI 中文摘要
本文建立了有限时域内全耦合非线性均值场前向-后向随机差分方程的可解性充分条件，该方程依赖于无条件一阶矩。前向递推使用下一后向状态的条件投影及其与创新的乘积。基于现有的支配-单调性方法，我们在中心坐标和均值坐标中构造确定性矩阵组合，并证明一个在同伦参数上一致的延拓估计。全局Lipschitz连续性和一个活跃的支配-强制方向产生唯一的平方可积适应解、一个先验界和系数稳定性。活跃参数可以被归一化，而无需对原始系数施加额外的小性限制。一个符号变换处理相反的单调性方向。一个具有饱和状态和均值相互作用的非线性例子验证了这些假设，包括退化支配方向。一个标量均值场LQ缓冲调整模型说明了该定理：其Hamiltonian解刻画了唯一的开环优化器。一个精确的有限情景树计算将该刻画与直接二次优化进行了对比验证。
英文摘要
This paper establishes sufficient conditions for finite-horizon solvability of fully coupled nonlinear mean-field forward--backward stochastic difference equations with dependence on unconditional first moments. The forward recursion uses conditional projections of the next backward state and its product with the innovation. Building on existing domination--monotonicity methods, we formulate deterministic matrix combinations in centered and mean coordinates and prove a continuation estimate uniform in the homotopy parameter. Global Lipschitz continuity and one active domination--coercivity direction yield a unique square-integrable adapted solution, an a priori bound, and coefficient stability. The active parameter can be normalized without imposing an additional smallness restriction on the original coefficients. A sign transformation handles the opposite monotonicity orientation. A nonlinear example with saturating state and mean interactions verifies the assumptions, including degenerate domination directions. A scalar mean-field LQ buffer-adjustment model illustrates the theorem: its Hamiltonian solution characterizes the unique open-loop optimizer. An exact finite scenario-tree calculation checks this characterization against direct quadratic optimization.
