Scaling limits of spatial compartment models for chemical reaction networks

DOI10.1214/14-AAP1070zbMath1329.60341arXiv1302.0774OpenAlexW2131942680MaRDI QIDQ894804

Lea Popovic, Peter Pfaffelhuber

Publication date: 24 November 2015

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.0774

zbMATH Keywords

scaling limitsmultiple time scalesstochastic averagingchemical reaction networkquasi-steady state assumption

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) (92C45) Chemical kinetics in thermodynamics and heat transfer (80A30) Functional limit theorems; invariance principles (60F17) Continuous-time Markov processes on discrete state spaces (60J27)

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Cites Work

• Unnamed Item
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• Exploring the performance of spatial stochastic simulation algorithms
• Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
• Asymptotic analysis of multiscale approximations to reaction networks
• High density limit theorems for nonlinear chemical reactions with diffusion
• Convergence of Markov chain approximations to stochastic reaction-diffusion equations
• Density-dependent limits for a nonlinear reaction-diffusion model
• Stochastic population growth in spatially heterogeneous environments
• Separation of time-scales and model reduction for stochastic reaction networks
• Stochastic modeling in nanoscale biophysics: subdiffusion within proteins
• Central limit theorems and diffusion approximations for multiscale Markov chain models
• Piecewise-Deterministic Markov Processes as Limits of Markov Jump Processes
• Stochastic reaction-diffusion kinetics in the microscopic limit
• Solutions of ordinary differential equations as limits of pure jump markov processes