The Lp Cauchy sequence for one-dimensional BSDEs with linear growth generators

TL;DR

This paper proves the existence of solutions in L^p space for one-dimensional BSDEs with linear growth generators by demonstrating that an approximation sequence is Cauchy in L^p.

Contribution

It introduces a direct method to establish the existence of solutions for BSDEs with linear growth generators in L^p spaces.

Findings

Existence of L^p solutions for one-dimensional BSDEs with linear growth.

Approximation sequences are shown to be Cauchy in L^p.

Provides a direct proof method for solutions in L^p spaces.

Abstract

In this paper, the existence of $L^p(p>1)$ solutions for one-dimensional backward stochastic differential equations will be shown directly by proving that an approximation sequence is a Cauchy one in the $L^p$ sense.