Conditional Backward Propagation of Chaos

TL;DR

This paper studies a backward stochastic differential equation influenced by the law of the solution conditioned on common noise, establishing well-posedness and propagation of chaos with convergence rates.

Contribution

It introduces a well-posedness framework for backward SDEs with law-dependent drivers under common noise and proves propagation of chaos with quantitative convergence estimates.

Findings

Existence and uniqueness of solutions under standard assumptions

Propagation of chaos with explicit convergence rates

Quantitative Wasserstein distance estimates

Abstract

In this paper, we first investigate the well-posedness of a backward stochastic differential equation where the driver depends on the law of the solution conditioned to a common noise. Under standard assumptions, we show that existence and uniqueness, as well as integrability results, still hold. We also study the associated interacting particles system, for which we prove propagation of chaos, with quantitative estimates on the rate of convergence in Wasserstein distance.