Before revision:  In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems  .
After revision:  In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems , and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians .