Weighted Bounded Mean Oscillation applied to Backward Stochastic Differential Equations

TL;DR

This paper develops new tail estimates for solutions of backward stochastic differential equations (BSDEs) using weighted bounded mean oscillation theory, covering quadratic and sub-quadratic cases, with applications to decoupling techniques.

Contribution

It introduces a novel approach using weighted bounded mean oscillation to derive tail estimates for BSDE solutions, extending existing methods.

Findings

Derived conditional Lp-estimates for BSDE solutions

Established new tail bounds for (Y,Z) processes

Enhanced decoupling techniques with new results

Abstract

We deduce conditional $L_p$-estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution $(Y,Z)$ on subintervals of $[0,T]$. Some new results for the decoupling technique introduced in \cite{jossain} are obtained as well and some applications of the tail estimates are given.