论文标题
在功能性中心极限定理上，均值不确定
On the functional central limit theorem with mean-uncertainty
论文作者
论文摘要
我们在规范空间$（\ Mathbb {r}^\ Mathbb {n}，\ Mathcal {b}（\ Mathbb {r}^\ Mathbb {n} n}）上引入了一个新的基本模型，用于独立且相同的分布式序列$（\ Mathbb {r}^\ Mathbb {n}，\ Mathcal {b}（\ Mathbb {r}^\ Mathbb {n}得益于定义明确的上和较低方差，我们通过Martingale Central Limit限制定理的方式获得了一个新的功能中心定理，并在经典概率理论中获得了随机积分的稳定性。然后，我们将其从规范空间扩展到一般的Sublinear期望空间。相应的证明是纯粹的概率，不依赖于非线性偏微分方程。
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined upper and lower variances, we obtain a new functional central limit theorem with mean-uncertainty by the means of martingale central limit theorem and stability of stochastic integral in the classical probability theory. Then we extend it from the canonical space to the general sublinear expectation space. The corresponding proofs are purely probabilistic and do not rely on the nonlinear partial differential equation.
