It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so long as the initial condition has strictly positive components). It is conjectured that the stochastically modeled analogs of these systems are positive recurrent. We prove this conjecture in the affirmative under the following additional assumptions: (i) the system is binary, and (ii) for each species, there is a complex (vertex in the associated reaction diagram) that is a multiple of that species. To show this result, a new proof technique is developed in which we study the recurrence properties of the n-step embedded discrete-time Markov chain.

中文翻译：

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具有单个连接类的随机建模弱可逆反应网络

近十年来，众所周知，确定性建模的反应网络是弱可逆且由单个链接类组成的，其轨迹从上方和下方均由正常数限定（只要初始条件具有严格的正分量）。据推测，这些系统的随机建模类似物是正循环的。我们在以下附加假设下肯定地证明了这个猜想：（i）系统是二元的，并且（ii）对于每个物种，都有一个复合物（相关反应图中的顶点）是该物种的倍数。为了证明这一结果，我们开发了一种新的证明技术，在该技术中我们研究了n步嵌入式​​离散时间马尔可夫链。