论文标题
部分可观测时空混沌系统的无模型预测
Coupling by reflection for controlled diffusion processes: turnpike property and large time behavior of Hamilton Jacobi Bellman equations
论文作者
论文摘要
我们研究了相应的随机控制问题的弱消散性半线性汉密尔顿 - 雅各比贝尔曼（HJB）方程的长期行为和收费公路。为此，我们根据适应受控扩散过程研究的反射来开发一种基于耦合变体的概率方法。我们证明了在峰值汉密尔顿 - 雅各比 - 贝尔曼方程的解决方案的存在和唯一性，以及在价值函数，最佳控制和最佳过程的水平下产生不同类型的定量指数收敛。此外，我们为具有独立感兴趣的HJB方程解决方案的解决方案提供了统一的时间梯度和HESSIAN估计。
We investigate the long time behavior of weakly dissipative semilinear Hamilton-Jacobi-Bellman (HJB) equations and the turnpike property for the corresponding stochastic control problems. To this aim, we develop a probabilistic approach based on a variant of coupling by reflection adapted to the study of controlled diffusion processes. We prove existence and uniqueness of solutions for the ergodic Hamilton-Jacobi-Bellman equation and different kind of quantitative exponential convergence results at the level of the value function, of the optimal controls and of the optimal processes. Moreover, we provide uniform in time gradient and Hessian estimates for the solutions of the HJB equation that are of independent interest.
