Before revision:  In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics , and determining moment bounds for the underlying stochastic process . Theoretical and computational solutions for these problems are obtained by utilizing a blend of ideas and techniques from probability theory, linear algebra , polynomial analysis and optimization theory.
After revision:  In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics . We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas and techniques from probability theory, linear algebra , polynomial analysis and optimization theory.