It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with ensembles of trajectories for long but fixed times, instead of states or configurations, to study dynamics of these Markovian stochastic processes and glean more information. In this paper we aim to show that the concept of ensemble of trajectories can be applied to a variety of stochastic models of gene expression ranging from a simple birth-death process to a more sophisticate model containing burst and switch. By considering the protein numbers as a relevant dynamical observable, apart from asymptotic behavior of remote tails of probability distribution, generating function for the cumulants of this observable can also be obtained. We discuss the unconditional stochastic Markov processes which generate the statistics of rare events in these models.

中文翻译：

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基因表达的随机建模：轨迹合奏的应用。

公认的是，基因表达可以建模为马尔可夫随机过程，因此适当的可观察物可能会受到较大的波动和罕见事件的影响。由于动力学通常不只是静力学，因此可以长时间但固定地处理一组轨迹，而不是状态或配置，以研究这些马尔可夫随机过程的动力学并收集更多信息。在本文中，我们旨在表明轨迹合奏的概念可以应用于从简单的生死过程到包含突发和切换的更复杂模型的各种基因表达随机模型。通过考虑蛋白质数量是一个相关的动态可观察到的现象，除了概率分布的遥远尾部的渐近行为，还可以得到这种可观察到的累积量的生成函数。我们讨论了在这些模型中生成罕见事件统计信息的无条件随机马尔可夫过程。