<p>This study addresses the nonlinear filtering problem for a class of multiscale McKean-Vlasov stochastic systems. First, by employing the Poisson equation method, we establish that the solution of the slow component of the multiscale system converges weakly to the solution of the corresponding averaging equation. Subsequently, we define the nonlinear filtering problems associated with both the original multiscale system and the averaging equation. Using the same Poisson equation approach, we further demonstrate the weak convergence between the nonlinear filter of the slow component in the original system and that of the averaging equation. Finally, an example is provided to illustrate our results.</p>

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

  • Huijie Qiao,
  • Wanlin Wei

摘要

This study addresses the nonlinear filtering problem for a class of multiscale McKean-Vlasov stochastic systems. First, by employing the Poisson equation method, we establish that the solution of the slow component of the multiscale system converges weakly to the solution of the corresponding averaging equation. Subsequently, we define the nonlinear filtering problems associated with both the original multiscale system and the averaging equation. Using the same Poisson equation approach, we further demonstrate the weak convergence between the nonlinear filter of the slow component in the original system and that of the averaging equation. Finally, an example is provided to illustrate our results.