| Autor: |
Anderson DF; University of Wisconsin-Madison, Wisconsin, USA. anderson@math.wisc.edu., Schnoerr D; Imperial College, London, UK., Yuan C; University of Wisconsin-Madison, Wisconsin, USA. |
| Jazyk: |
angličtina |
| Zdroj: |
Journal of mathematical biology [J Math Biol] 2020 May; Vol. 80 (6), pp. 1919-1951. Date of Electronic Publication: 2020 Mar 24. |
| DOI: |
10.1007/s00285-020-01485-y |
| Abstrakt: |
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). |
| Databáze: |
MEDLINE |
| Externí odkaz: |
|
Full text from SpringerLink