Ergodic BSDEs driven by G-Brownian motion and applications

This paper considers a new kind of backward stochastic differential equations (BSDEs) driven by [Formula: see text]-Brownian motion, which is called ergodic [Formula: see text]-BSDEs. Firstly, the well-posedness of [Formula: see text]-BSDEs with infinite horizon is given by combining a new linearization method with the argument of Briand and Hu [4]. Then, in view of [Formula: see text]-stochastic calculus approach the Feynman–Kac formula for fully nonlinear elliptic partial differential equations (PDEs) is established. Finally, with the help of the aforementioned results we obtain the existence of solution to [Formula: see text]-EBSDE and some applications are also stated.