# Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games in an Infinite Horizon

arXiv: https://arxiv.org/abs/1404.7220 · HTML: https://mlsanity.com/paper/1404.7220/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics](https://mlsanity.com/paper/2402.04721/) (2024)
- [Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons](https://mlsanity.com/paper/2602.08075/) (2026)

## Abstract (arXiv)

This paper is concerned with a linear quadratic stochastic two-person zero-sum differential game with constant coefficients in an infinite time horizon. Open-loop and closed-loop saddle points are introduced. The existence of closed-loop saddle points is characterized by the solvability of an algebraic Riccati equation with a certain stabilizing condition. A crucial result makes our approach work is the unique solvability of a class of linear backward stochastic differential equations in an infinite horizon.