论文标题
多尺度McKean-Vlasov随机系统的非线性过滤的强近似
Strong approximation of nonlinear filtering for multiscale McKean-Vlasov stochastic systems
论文作者
论文摘要
这项工作涉及多尺度McKean-Vlasov随机系统的非线性过滤问题，其中整个系统都取决于快速组件的分布。首先，我们证明原始系统的慢组分会收敛到$ l^{2p} $（$ p \ geqslant 1 $）的平均系统。此外，我们为$ l^2 $案件获得了强大的收敛顺序。然后，考虑到一个观察过程，取决于慢组分及其分布，我们表明，慢速组件及其分布的非线性过滤也会收敛于$ l^{q} $中的平均系统的非线性过滤（$ p \ geq 8，1 \ leq q \ leq q \ leq q \ leq \ leq \ leq \ frac {p} p} {8} {8} {8} $）。
This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system converges to an average system in the $L^{2p}$ ($p\geqslant 1$) sense. Moreover, we obtain the strong convergence order for the $L^2$ case. Then, given an observation process which depends on the slow component and its distribution, we show that the nonlinear filtering of the slow component and its distribution also converges to that of the average system in the $L^{q}$ ($p\geq 8, 1\leq q\leq \frac{p}{8}$) sense.
