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 and hence , apart from asymptotic behavior of remote tails of probability distributions of the dynamical observables, generating functions for the cumulants of these observables can easily be obtained. We start with the simplest stochastic model of gene expression and then extend our approach to more sophisticated and yet more realistic models.
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.
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and hence
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
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distributions of the dynamical observables, generating functions
distribution, generating function
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these observables can easily
this observable can also
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start with the simplest stochastic model of gene expression and then extend our approach to more sophisticated and yet more realistic
discuss the unconditional stochastic Markov processes which generate the statistics of rare events in these