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On the McKean‐Vlasov Limit for Interacting Diffusions
Author(s) -
Gärtner Jürgen
Publication year - 1988
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19881370116
Subject(s) - mathematics , uniqueness , monotonic function , martingale (probability theory) , smoothness , law of large numbers , coercivity , mathematical analysis , diffusion process , limit (mathematics) , physics , condensed matter physics , knowledge management , statistics , innovation diffusion , random variable , computer science
For a system of diffusions in a domain of R d with long‐range weak interaction the behavior of the associated empirical process is studied. Under mild growth and smoothness assumptions on the drift and diffusion coefficients such as coercivity and monotonicity conditions the law of large numbers and the propagation of chaos are proved. Existence and uniqueness of the weak solution to the McKean ‐ Vlasov equation and the associated non‐linear martingale problem are investigated.