On the Generalized Sylvester Polynomials

Özmen, Nejla; Erkuş-Duman, Esra

doi:10.1007/978-3-030-04459-6_5

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2019

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“…C n (j;x) is the Poisson-Charlier polynomial defined explicitly by [27] (24) for x > 0. These polynomials are a family of orthogonal polynomials satisfying the following relation…”

Section: Modelmentioning

confidence: 99%

Stochastic modeling of gene expression: application of ensembles of trajectories

Torkaman

Jafarpour²

2019

Phys. Biol.

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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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“…C n (j;x) is the Poisson-Charlier polynomial defined explicitly by [27] (24) for x > 0. These polynomials are a family of orthogonal polynomials satisfying the following relation…”

Section: Modelmentioning

confidence: 99%

Stochastic modeling of gene expression: application of ensembles of trajectories

Torkaman

Jafarpour²

2019

Phys. Biol.

View full text Add to dashboard Cite

show abstract

On the Generalized Sylvester Polynomials

Cited by 1 publication

References 1 publication

Stochastic modeling of gene expression: application of ensembles of trajectories

Stochastic modeling of gene expression: application of ensembles of trajectories

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