Chaoticity for Multiclass Systems and Exchangeability Within Classes

DOI10.1239/jap/1231340243zbMath1154.60357arXiv0709.1918OpenAlexW2032161938MaRDI QIDQ5504171

Carl Graham

Publication date: 21 January 2009

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

Full work available at URL: https://arxiv.org/abs/0709.1918

zbMATH Keywords

de Finetti's theoremmixturesinteracting particle systemmultispeciespartial exchangeabilitymultitypechaoticitymulticlassconvergence of empirical measuresdirecting measureHewitt-Savage 0-1 law

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Convergence of probability measures (60B10) Sufficient statistics and fields (62B05) Exchangeability for stochastic processes (60G09)

Related Items (11)

Multi-class oscillating systems of interacting neurons ⋮ White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps ⋮ Convergence of multi-class systems of fixed possibly infinite sizes ⋮ Self-adaptive congestion control for multiclass intermittent connections in a communication network ⋮ Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks ⋮ Spiking neurons : interacting Hawkes processes, mean field limits and oscillations ⋮ Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels ⋮ RESILIENCE TO CONTAGION IN FINANCIAL NETWORKS ⋮ Managing Default Contagion in Inhomogeneous Financial Networks ⋮ Propagation of chaos and Poisson hypothesis ⋮ Interacting multi-class transmissions in large stochastic networks

Cites Work

• Finite exchangeable sequences
• McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets
• Uses of exchangeability
• The mathematical theory of dilute gases
• Canonical representations and convergence criteria for processes with interchangeable increments
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