Classical solution of path-dependent mean-field semilinear PDEs

TL;DR

This paper develops a novel method to construct classical solutions for path-dependent PDEs with coefficients depending on paths and measures, advancing the understanding of non-Markovian mean-field systems.

Contribution

It introduces the 'parameter frozen' technique to solve complex path-dependent PDEs involving path and measure dependence.

Findings

Successfully constructs classical solutions for the PPDEs.

Introduces the 'parameter frozen' approach for handling path dependencies.

Provides a framework for analyzing large-scale non-Markovian mean-field systems.

Abstract

The paper concerns classical solution of path-dependent partial differential equations (PPDEs) with coefficients depending on both variables of path and path-valued measure, which are crucial to understanding large-scale mean-field interacting systems in a non-Markovian setting. We construct classical solutions of the PPDEs via solution of the forward and backward stochastic differential equations. To accommodate the intricacies introduced by the appearance of the path in the coefficients, we develop a novel technique known as the ``parameter frozen'' approach to the PPDEs.