arXiv subjects

Wanlin Wei

Publications and source records attributed to Wanlin Wei.

2 recordsLinked to original sources

arXiv2022

Weak approximation of nonlinear filtering for multiscale McKean-Vlasov stochastic systems

The work concerns the nonlinear filtering problem for a class of multiscale McKean-Vlasov stochastic systems. First of all, by a Poisson equation we prove that the solution of the slow part for a multiscale system weakly converges to the solution of the average equation. Then we define nonlinear filtering of the origin multiscale system and the average equation, and again through the same Poisson equation show the weak approximation between nonlinear filtering of the slow part for the origin multiscale system and that of the average equation.

math.PR↗

arXiv2022

Strong approximation of nonlinear filtering for multiscale McKean-Vlasov stochastic systems

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.

math.PR↗