Stochastic Markov models for the process of binary complex formation and dissociation

We consider the chemical reaction $A+B\rightleftarrows AB$ taking place in a compartment of volume $V$, which contains $M$ and $N$, $M\geq N$, particles of species $A$ and $B$ free or bound. We investigate two stochastic models for the reaction, the quadratic model and the linear model. These models are homogeneous birth and death processes with a state space $\{0,1,\dots,N\}$. We derive inequalities which allow to estimate the accuracy of approximation of the state probability vectors, both transient and stationary, of the quadratic model by the state probability vectors of the linear model at $M$ $V\to\infty$, $V^{-1}M={\rm const}$. We show that if $N$ is small these inequalities can provide bounds which are of order of exact values of the difference norms of the corresponding state probability vectors.