AI 中文总结
研究切换扩散的状态索引半群块非参数估计，用Dynkin--Taylor展开等方法确定相关系数，收缩网格下得到渐近正态估计量，支持短时间近似等，固定网格局部多项式理论和数值研究作补充。
AI 中文摘要
状态条件转移概率和矩是混合系统预测和决策的基本输入，但它们的短时无穷小结构不可直接观测。我们研究了与状态一起观测的切换扩散的状态索引半群块的非参数估计。通过Dynkin-Taylor展开确定前两个块生成器系数，局部探针恢复切换强度、漂移和扩散。在收缩网格下，一个共同设计的差异消除了局部水平并产生一个鞅阵列；不重叠的二阶差分保留块内协方差并产生方差因子2。由此产生的一阶和二阶估计量是渐近正态的，允许可行的学生化，并支持对原始系数之间相互作用的短时间近似和规格检查。固定网格局部多项式理论和数值研究补充了恢复结果。
英文摘要
Regime-conditioned transition probabilities and moments are basic inputs for prediction and decision making in hybrid systems, but their short-time infinitesimal structure is not directly observable. We study nonparametric estimation of regime-indexed semigroup blocks for switching diffusions observed together with their regimes. A Dynkin--Taylor expansion identifies the first two block-generator coefficients, and localized probes recover switching intensities, drift, and diffusion. Under shrinking meshes, a common-design difference cancels the localized level and yields a martingale array; nonoverlapping second differences preserve within-block covariance and produce the variance factor two. The resulting first- and second-order estimators are asymptotically normal, admit feasible studentization, and support short-horizon approximation and specification checks for interactions among primitive coefficients. Fixed-mesh local-polynomial theory and a numerical study complement the recovery results.
