Asymptotic problems for viscous Hamilton-Jacobi equations with random coefficients

在本研究中，我们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组，称为粘性Hamilton-Jacobi方程。更具体地说，我们用解析法和概率法研究了解的长期行为。结果表明，随着时间趋于无限，解会收敛到稳定状态。我们还成功地用遍历随机控制问题刻画了这种稳态

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