Asymptotic problems for viscous Hamilton-Jacobi equations with random coefficients

本文研究了随机最优控制问题中出现的一类非线性偏微分方程，即粘性Hamilton-Jacobi方程。更具体地说，我们通过分析和概率方法研究了解决方案的长期行为。结果表明，当时间趋于无穷时，解收敛于稳态。我们也成功地用遍历随机控制问题来描述这种稳态

In this research, we dealt with a class of nonlinear partial differential equations, called viscous Hamilton-Jacobi equations, which appear in stochastic optimal control problems. More specifically, we investigated the long-time behavior of solutions by both analytical and probabilistic approaches. It turned out that solutions converge to a steady state as time tends to infinity. We also succeeded in characterizing such steady state in terms of ergodic stochastic control problems