L^p-estimate for mean-field type FBSDEs

¹ School of Mathematics, Shandong University, Jinan 250100, PR China
² School of Mathematics and Statistics, Shandong University, Weihai 264209, PR China

^* Corresponding author: yuzhiyong@sdu.edu.cn

Received: 4 March 2024
Accepted: 7 August 2025

Abstract

This paper is concerned with the L^p-regularity (p > 2) of mean-field type forward–backward stochastic differential equations (MF-FBSDEs, for short). For three classes of nonlinear MF-FBSDEs, linear MF-FBSDEs and linear Hamiltonian systems, we obtain three L^p-results, respectively. Each L^p-result includes the existence, estimate and continuous dependence on parameters of solutions in the sense of p-th power integrability. In the third case, we also provide an L^p-result for the optimal controls of a class of mean-field type linear-quadratic (MF-LQ, for short) problems with random coefficient matrices.