A system of nonlinear equations with application to large deviations for Markov chains with finite lifetime

Ze-Chun Hu, Wei Sun, Jing Zhang

In this paper, we first show the existence of solutions to the following system of nonlinear equations \begin{eqnarray*}\left\{\begin{array}{l} a_{11}x_1+a_{12}x_2+a_{13}x_3+\cdots…