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Multilevel large deviations and interacting diffusions
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  • Published: December 1994

Multilevel large deviations and interacting diffusions

  • D. A. Dawson1 &
  • J. Gärtner2,3 

Probability Theory and Related Fields volume 98, pages 423–487 (1994)Cite this article

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  • 20 Citations

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Summary

Let (ξN) be a sequence of random variables with values in a topological space which satisfy the large deviation principle. For eachM and eachN, let ΞM, N denote the empirical measure associated withM independent copies of ξN. As a main result, we show that (ΞM, N) also satisfies the large deviation principle asM,N→∞. We derive several representations of the associated rate function. These results are then applied to empirical measure processes ΞM, N(t) =M −1 Σ Ni=1 δξ N i (t) 0≦t≦T, where (ξ N1 ,..., ξ N M (t)) is a system of weakly interacting diffusions with noise intensity 1/N. This is a continuation of our previous work on the McKean-Vlasov limit and related hierarchical models ([4], [5]).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Carleton University Ottawa, K1S 5B6, Ottawa, Canada

    D. A. Dawson

  2. Institut für Angewandte Analysis und Stochastik, D-10117, Berlin, Germany

    J. Gärtner

  3. Mathematik, Technische Universität, FB, Strasse des 17. Juni 136, D-10623, Berlin, Germany

    J. Gärtner

Authors
  1. D. A. Dawson
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  2. J. Gärtner
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Additional information

Research partially supported by a Natural Science and Engineering Research Council of Canada operating grant

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Dawson, D.A., Gärtner, J. Multilevel large deviations and interacting diffusions. Probab. Th. Rel. Fields 98, 423–487 (1994). https://doi.org/10.1007/BF01192835

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  • Received: 13 July 1992

  • Revised: 05 November 1993

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01192835

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Mathematics Subject Classification

  • 60F10
  • 60k35
  • 60J60
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