ArticleJournal of mathematical biology2020
Time-dependent product-form Poisson distributions for reaction networks with higher order complexes.
Article in Journal of mathematical biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed, 9 citations in OpenAlex.
- Solving stochastic gene-expression models using queueing theory: A tutorial review.Biophysical journal · 2024Review
- Incorporating age and delay into models for biophysical systems.Physical biology · 2021Article
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3 authors at 2 institutions in 2 countries.
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Abstract
It is well known that stochastically modeled reaction networks that are complex balanced admit a stationary distribution that is a product of Poisson distributions. In this paper, we consider the following related question: supposing that the initial distribution of a stochastically modeled reaction network is a product of Poissons, under what conditions will the distribution remain a product of Poissons for all time? By drawing inspiration from Crispin Gardiner's "Poisson representation" for the solution to the chemical master equation, we provide a necessary and sufficient condition for such a product-form distribution to hold for all time. Interestingly, the condition is a dynamical "complex-balancing" for only those complexes that have multiplicity greater than or equal to two (i.e. the higher order complexes that yield non-linear terms to the dynamics). We term this new condition the "dynamical and restricted complex balance" condition (DR for short).
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