Long-time behavior of stochastic multimolecular reaction model

In the paper, we focus on asymptotic behavior of a stochastic multimolecular reaction model. Our main goal is not only to prove the permanence of the reaction but also to estimate the polynomial convergence rate of the transition probability to an invariant probability measure. Our result gives a precise characterization of the rate with which the different powers of a test function converges in terms of the exponent. The rate of convergence is proved to be bounded above by any polynomial decay.