Product-Form Poisson-Like Distributions and Complex Balanced Reaction Systems

DOI10.1137/15M1029916zbMath1337.92085arXiv1507.02195OpenAlexW1577069328WikidataQ64004732 ScholiaQ64004732MaRDI QIDQ2790413

Carsten Wiuf, Daniele Cappelletti

Publication date: 4 March 2016

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02195

zbMATH Keywords

Markov processstationary distributionODE systembiochemical reaction networkmass-action systemdeficiency theory

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Classical flows, reactions, etc. in chemistry (92E20) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Chemical kinetics in thermodynamics and heat transfer (80A30) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (23)

An Algebraic Approach to Product-form Stationary Distributions for Some Reaction Networks ⋮ Large deviations theory for Markov jump models of chemical reaction networks ⋮ Prevalence of deficiency-zero reaction networks in an Erdös–Rényi framework ⋮ Time-dependent product-form Poisson distributions for reaction networks with higher order complexes ⋮ Finite Time Distributions of Stochastically Modeled Chemical Systems with Absolute Concentration Robustness ⋮ Computational Translation Framework Identifies Biochemical Reaction Networks with Special Topologies and Their Long-Term Dynamics ⋮ On balance relations for irreversible chemical reaction networks ⋮ Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics ⋮ On classes of reaction networks and their associated polynomial dynamical systems ⋮ Detailed balance \(=\) complex balance \(+\) cycle balance: a graph-theoretic proof for reaction networks and Markov chains ⋮ Stochastically modeled weakly reversible reaction networks with a single linkage class ⋮ Tier structure of strongly endotactic reaction networks ⋮ Deficiency zero for random reaction networks under a stochastic block model framework ⋮ Non-explosivity of stochastically modeled reaction networks that are complex balanced ⋮ Product-form stationary distributions for deficiency zero networks with non-mass action kinetics ⋮ Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions ⋮ Graphically Balanced Equilibria and Stationary Measures of Reaction Networks ⋮ The dynamics of stochastic mono-molecular reaction systems in stochastic environments ⋮ Stationary distributions via decomposition of stochastic reaction networks ⋮ Product-form estimators: exploiting independence to scale up Monte Carlo ⋮ Stationary Distributions and Condensation in Autocatalytic Reaction Networks ⋮ Discrepancies between extinction events and boundary equilibria in reaction networks ⋮ Results on stochastic reaction networks with non-mass action kinetics

Cites Work

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• Product-form stationary distributions for deficiency zero chemical reaction networks
• Lyapunov functions, stationary distributions, and non-equilibrium potential for reaction networks
• Identifiability of chemical reaction networks
• Asymptotic analysis of multiscale approximations to reaction networks
• Strong approximation theorems for density dependent Markov chains
• Separation of time-scales and model reduction for stochastic reaction networks
• Dynamical properties of discrete reaction networks
• Stochastic Analysis of Biochemical Systems
• Networks of Waiting Lines
• Deficiency Zero Petri Nets and Product Form

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