Mean Field Limits of Particle-Based Stochastic Reaction-Diffusion Models

DOI10.1137/20M1365600zbMath1482.35115arXiv2003.11868OpenAlexW3013862997MaRDI QIDQ5024686

Jingwei Ma, Samuel A. Isaacson, Konstantinos V. Spiliopoulos

Publication date: 27 January 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.11868

zbMATH Keywords

mean field approximationchemical reaction networksparticle modelscoarse-grained deterministic partial integro-differential equation

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting particle systems in time-dependent statistical mechanics (82C22) Reaction-diffusion equations (35K57) Theoretical approximation in context of PDEs (35A35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs with randomness, stochastic partial differential equations (35R60) Integro-partial differential equations (35R09)

Related Items

Chemical diffusion master equation: Formulations of reaction–diffusion processes on the molecular level, A probabilistic framework for particle-based reaction-diffusion dynamics using classical Fock space representations, A Route to the Hydrodynamic Limit of a Reaction-Diffusion Master Equation Using Gradient Structures, Finding analytical approximations for discrete, stochastic, individual-based models of ecology, Fluctuation analysis for particle-based stochastic reaction-diffusion models, A spatial measure-valued model for chemical reaction networks in heterogeneous systems, A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition, Large deviations for interacting multiscale particle systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lévy flights in evolutionary ecology
• Heterogeneous credit portfolios and the dynamics of the aggregate losses
• On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
• Stopping times and tightness
• McKean-Vlasov limit for interacting random processes in random media.
• Large deviations and mean-field theory for asymmetric random recurrent neural networks
• Default clustering in large portfolios: typical events
• A new approach to quantitative propagation of chaos for drift, diffusion and jump processes
• An unstructured mesh convergent reaction-diffusion master equation for reversible reactions
• Particle systems with a singular mean-field self-excitation. Application to neuronal networks
• Multidimensional diffusion processes.
• From interacting agents to density-based modeling with stochastic PDEs
• Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
• Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component
• A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning
• Weak convergence of sequences of semimartingales with applications to multitype branching processes
• A criterion of convergence of measure‐valued processes: application to measure branching processes
• Deterministic limit of the stochastic model of chemical reactions with diffusion
• How Reaction-Diffusion PDEs Approximate the Large-Population Limit of Stochastic Particle Models
• Quantitative Propagation of Chaos in a Bimolecular Chemical Reaction-Diffusion Model
• LARGE PORTFOLIO ASYMPTOTICS FOR LOSS FROM DEFAULT
• Stochastic Analysis of Biochemical Systems
• Stochastic Models for Structured Populations