A stochastic particle system: Fluctuations around a nonlinear reaction- diffusion equation

DOI10.1016/0304-4149(88)90081-6zbMath0654.60098OpenAlexW2046181329MaRDI QIDQ1108697

Peter Dittrich

Publication date: 1988

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(88)90081-6

zbMATH Keywords

central limit theoremreaction-diffusion equationreflecting boundary conditionsinfinite- dimensional Ornstein-Uhlenbeck processpropagation of chaos expansion

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60) Random measures (60G57) Functional limit theorems; invariance principles (60F17)

Related Items

Fluctuations for annihilations of Brownian spheres, Fluctuation limit for interacting diffusions with partial annihilations through membranes, On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes, Functional central limit theorem for Brownian particles in domains with Robin boundary condition, Markov properties of the fluctuation limit of a particle system with death, Fluctuations of one-dimensional Ginzburg-Landau models in nonequilibrium, Nonequilibrium fluctuations in particle systems modelling reaction- diffusion equations, Stability of a class of transformations of distribution-valued processes and stochastic evolution equations, Scaling limits of interacting diffusions in domains, Unscaled spatial branging process with interaction: macrospic equation and local equilibrium

Cites Work

• Collective phenomena in interacting particle systems
• Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev
• High density limit theorems for nonlinear chemical reactions with diffusion
• A stochastic model of a chemical reaction with diffusion
• Limit laws for a coagulation model of interacting random particles
• Law of large numbers and central limit theorem for linear chemical reactions with diffusion
• Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-limit
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