# Stochastic Gronwall's inequality in random time horizon and its application to BSDE

## TL;DR

This paper extends Gronwall's inequality to stochastic settings with random time horizons and applies it to establish comparison results for BSDEs with random terminal times.

## Contribution

It introduces a stochastic Gronwall's inequality applicable to unbounded random time horizons and uses it to prove a comparison theorem for BSDEs with stochastic monotonicity.

## Key findings

- Established a stochastic Gronwall's inequality for unbounded random time horizons.
- Proved a comparison theorem for BSDEs with random terminal time.
- Demonstrated the inequality's application in stochastic analysis.

## Abstract

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under stochastic monotonicity condition.

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Source: https://tomesphere.com/paper/1903.09902