@article{CW2016siam,
 abstract = {Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on \$ℕ^n\$. Here we provide a fundamental characterization that connects structural properties of a network to its dynamical features. Specifically, we define the notion of “stochastically complex balanced systems” in terms of the network's stationary distribution and provide a characterization of stochastically complex balanced systems, parallel to that established in the 1970s and 1980s for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the “deficiency zero theorem” and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and we explore the possibility to characterize complex balanced systems in terms of product-form Poisson-like stationary distributions.},
 author = {Cappelletti, D. and Wiuf, C.},
 doi = {10.1137/15M1029916},
 journal = {SIAM Journal on Applied Mathematics},
 keywords = {reaction networks; continuous time Markov chains; stationary distribution; ordinary differential equations; deficiency theory},
 month = {01},
 number = {1},
 pages = {411-432},
 title = {Product-form poisson-like distributions and complex balanced reaction systems},
 url = {https://doi.org/10.1137/15M1029916},
 volume = {76},
 year = {2016}
}