@article{ref1,
title="Time-dependent product-form Poisson distributions for reaction networks with higher order complexes",
journal="Journal of Mathematical Biology",
year="2020",
author="Anderson, David F. and Schnoerr, David and Yuan, Chaojie",
volume="ePub",
number="ePub",
pages="ePub-ePub",
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 &quot;Poisson representation&quot; 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 &quot;complex-balancing&quot; 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 &quot;dynamical and restricted complex balance&quot; condition (DR for short).<p /> <p>Language: en</p>",
language="en",
issn="0303-6812",
doi="10.1007/s00285-020-01485-y",
url="http://dx.doi.org/10.1007/s00285-020-01485-y"
}