2010/07/19 by Tuǧrul Dayar, Dayar, Tugrul, Holger Hermanns +5
Biochemistry, Genetics and Molecular Biology · #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Numerical Analysis (math.NA) #Probability (math.PR) #Quantitative Methods (q-bio.QM)
paper · pdf · doi:10.48550/arxiv.1007.3130
openalex publication_date 2010/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its function as a biological switch. Unfortunately, the state space of these systems is infinite in most cases, preventing the use of traditional steady state solution techniques. In this paper we develop a new approach to tackle this problem by first retrieving geometric bounds enclosing a major part of the steady state probability mass, followed by a more detailed analysis revealing state-wise bounds.