Optimal Filtering for Interacting Particle Systems

TL;DR

This paper develops a novel approach to optimal filtering in interacting particle systems using Malliavin calculus, transforming the problem into an optimal control framework and deriving necessary conditions for the filter coefficients.

Contribution

It introduces a new method leveraging Malliavin calculus to analyze and solve the optimal filtering problem for interacting particle systems, providing a theoretical foundation for filter coefficient characterization.

Findings

Derived the differential equation for the covariance process.

Transformed the filtering problem into an optimal control problem.

Established necessary conditions for the filter coefficients.

Abstract

In this paper, we study the optimal filtering problem for a interacting particle system generated by stochastic differential equations with interaction. By using Malliavin calculus, we construct the differential equation of the covariance process and transform the filter problem to an optimal control problem. Finally we give the necessary condition that the coefficient of the optimal filter should satisfy