Stationary Solutions of SPDEs and Infinite Horizon BDSDEs with Non-Lipschitz Coefficients

Qi Zhang, Huaizhong Zhao

We prove a general theorem that the $L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^1)\otimes L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^d)$ valued solution of an infinite horizon backward doubl…