Multidimensional Infinite-Horizon Markovian Backward Stochastic Differential Equations with Continuous Coefficients and Nonzero-Sum Differential Games

This paper addresses the solvability of multidimensional infinite-horizon Markovian backward stochastic differential equations with continuous coefficients. We do not require the Lipschitz property or other quantitative controls of differences, and each component of the generator is allowed to depend simultaneously on all components of the multidimensional backward variables. A local L^q-domination framework adapted to the infinite-horizon setting is developed and combined with our linear flow conjugacy analysis to obtain the required distributional control in the presence of unbounded linear drift. We also derive a common Markov representation valid for the entire family of initial states. The analytical obstacles arising from weak regularity and the multidimensional structure are thereby overcome. Furthermore, we consider a class of infinite-horizon nonzero-sum differential games with a general non linear structure, allowing player controls to be fully coupled and permitting payoff criteria that are not restricted to an exponential discount form, establish an equivalence between the game and the corresponding multidimensional infinite-horizon backward stochastic differential equations, and prove the existence of a Nash equilibrium.