SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 1152-1164, April 2024.
Abstract. We consider the infinite horizon optimal control problems of the controlled Markov process. We verify the relationship between the controlled Markov process and its fluid limit by the viscosity solution approach. More precisely, we show that the value function of the controlled Markov process converges to one of its limit processes which is the viscosity solution of the associated Hamilton–Jacobi–Bellman equation.

中文翻译：

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具有吸收边界的 Hamilton-Jacobi-Bellman 方程的马尔可夫链逼近

SIAM 控制与优化杂志，第 62 卷，第 2 期，第 1152-1164 页，2024 年 4 月。
摘要。我们考虑受控马尔可夫过程的无限视野最优控制问题。我们通过粘度求解方法验证了受控马尔可夫过程与其流限之间的关系。更准确地说，我们表明受控马尔可夫过程的价值函数收敛于其极限过程之一，即相关的 Hamilton-Jacobi-Bellman 方程的粘度解。