Forward-backward stochastic differential equations on infinite horizon and quasilinear elliptic PDEs

© 2019 Elsevier Inc. A class of infinite horizon forward-backward stochastic differential equations (FBSDEs) is investigated. Under some monotonicity conditions, the existence and uniqueness of solutions in an arbitrarily large space for FBSDEs on infinite horizon is obtained. The probabilistic interpretations for a large class of quasilinear elliptic partial differential equations (PDEs) in a global space is then given by virtue of the solutions of FBSDEs on infinite horizon.