SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2050-2077, January 2020.
In this paper we study an Ergodic Markovian BSDE involving a forward process $X$ that solves an infinite dimensional forward stochastic evolution equation with multiplicative and possibly degenerate diffusion coefficient. A concavity assumption on the driver allows us to avoid the typical quantitative conditions relating the dissipativity of the forward equation and the Lipschitz constant of the driver. Although the degeneracy of the noise has to be of a suitable type, we can give a stochastic representation of a large class of Ergodic HJB equations; moreover, our general results can be applied to achieve the synthesis of the optimal feedback law in relevant examples of ergodic control problems for SPDEs.

中文翻译：

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具有乘性和简并噪声的遍历BSDE

SIAM控制与优化杂志，第58卷，第4期，第2050-2077页，2020
年1月。在本文中，我们研究了涉及正向过程$ X $的遍历马尔可夫BSDE，它可以解无穷维正向随机演化方程，并且具有可乘性，并且可能退化扩散系数。对驱动程序的凹度假设使我们能够避免与正向方程的耗散性和驱动程序的Lipschitz常数相关的典型定量条件。尽管噪声的简并性必须是合适的类型，但是我们可以给出一大类遍历HJB方程的随机表示。此外，我们的一般结果可用于在SPDE遍历控制问题的相关示例中实现最佳反馈定律的综合。