Limit theorems for generalized density-dependent Markov chains and bursty stochastic gene regulatory networks

DOI10.1007/s00285-019-01445-1zbMath1431.60083arXiv1909.00038OpenAlexW2989649925WikidataQ91389136 ScholiaQ91389136MaRDI QIDQ2299270

Chen Jia, Xian Chen

Publication date: 21 February 2020

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.00038

zbMATH Keywords

martingale problemstochastic gene expressionpiecewise deterministic Markov processLévy-type operatorrandom burst

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Biochemistry, molecular biology (92C40) Martingales with continuous parameter (60G44) Continuous-time Markov processes on discrete state spaces (60J27) General biology and biomathematics (92B05) Systems biology, networks (92C42) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (7)

Fast reactions with non-interacting species in stochastic reaction networks ⋮ Inference on autoregulation in gene expression with variance-to-mean ratio ⋮ Full classification of dynamics for one-dimensional continuous-time Markov chains with polynomial transition rates ⋮ Analytic solutions for stochastic hybrid models of gene regulatory networks ⋮ Detailed balance, local detailed balance, and global potential for stochastic chemical reaction networks ⋮ A data-driven method to learn a jump diffusion process from aggregate biological gene expression data ⋮ Heavy-tailed distributions in a stochastic gene autoregulation model

Cites Work

• Reflection couplings and contraction rates for diffusions
• On time reversal of piecewise deterministic Markov processes
• Regularity of semigroups generated by Lévy type operators via coupling
• On ergodicity of some Markov processes
• Strong approximation theorems for density dependent Markov chains
• Simple mathematical models of gene regulatory dynamics
• Dynamic Behavior of Stochastic Gene Expression Models in the Presence of Bursting
• Equivalence of Stochastic Equations and Martingale Problems
• Dynamics and density evolution in piecewise deterministic growth processes
• [https://portal.mardi4nfdi.de/wiki/Publication:4043914 Diffusion processes associated with L�vy generators]
• Stochastic Analysis of Biochemical Systems
• Limit theorems for sequences of jump Markov processes approximating ordinary differential processes
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