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Occupation times in systems of null recurrent Markov processes
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  • Published: June 1994

Occupation times in systems of null recurrent Markov processes

  • Tzong-Yow Lee1 &
  • Bruno Remillard2 

Probability Theory and Related Fields volume 98, pages 245–259 (1994)Cite this article

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  • 3 Citations

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Summary

We study asymptotic properties of differences of occupation times for infinite systems of noninteracting Markovian particles. Under a suitable normalisation we prove convergence in law to a nondegerate Gaussian field. We also obtain large deviations properties. These results generalise previous results obtained separately by both authors.

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References

  1. Cox, J.T., Durrett, R.: Large deviations for independent random walks. Probab. Theory Relat. Fields84, 67–82 (1990)

    Google Scholar 

  2. Dawson, D., Gärtner, J.: Large deviations for McKean-Vlasov limit of weakly interacting diffusions. Stochastics20, 247–308 (1987)

    Google Scholar 

  3. Feller, W.: An introduction to probability theory and its applications, vol. 2. New York: Wiley 1971

    Google Scholar 

  4. Kasahara, Y.: Limit theorems of occupation times for Markov processes. Publ. RIMS. Kyoto Univ.12, 801–818 (1977)

    Google Scholar 

  5. Lee, T.-Y.: Large deviations for systems of noninteracting recurrent particles. Ann. Probab.17, 46–57 (1989)

    Google Scholar 

  6. Remillard, B.: Asymptotic behaviour of the Laplace transform of weighted occupation times of random walks and applications. In: Pinsky, M.A. (ed.) Diffusion Processes and Related Problems in Analysis, vol. 1. Progress in Probability vol. 22, pp. 497–519. Boston: Birkäuser 1990

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, 20742, Maryland, MD, USA

    Tzong-Yow Lee

  2. Department de mathématiques, Université du Québec à Trois-Rivières, G1K 7P4, Trois-Rivières, Québec, Canada

    Bruno Remillard

Authors
  1. Tzong-Yow Lee
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  2. Bruno Remillard
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Additional information

Supported in part by the Office of Graduate Studies and Research (1990), University of Maryland and by NSF Grant No. DMS 9207928

Supported in part by the Fonds Institutionnel de Recherche, Université du Québec à Trois-Rivières and by the Natural Sciences and Engineering Research Council of Canada, Grant No. OGP0042137

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Cite this article

Lee, TY., Remillard, B. Occupation times in systems of null recurrent Markov processes. Probab. Th. Rel. Fields 98, 245–259 (1994). https://doi.org/10.1007/BF01192516

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  • Received: 29 March 1993

  • Revised: 22 October 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192516

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Mathematics Subject Classifications (1985)

  • Primary 60F10
  • secondary 60J05
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