Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON THE LARGE DEVIATION PROPERTY OF RANDOM MEASURES ON THE d-DIMENSIONAL EUCLIDEAN SPACE

  • Hwang, Dae-Sik (Department of Mathematics, Faculty Board, Air Force Academy)
  • Published : 2002.01.01
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Abstract

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

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References

  1. Statist. Probab. Lett. v.9 Large deviations for some weakly dependent random process R. M. Burton;H. Dehling https://doi.org/10.1016/0167-7152(90)90031-2
  2. Stochastics v.20 Large deviations from the Mackean-Vlasov limit for weakly interacting diffusions D. A. Dawson;J. Gartner https://doi.org/10.1080/17442508708833446
  3. Large deviations techniques and applications A. Dembo;O. Zeitouni
  4. Large deviations J. D. Deuschel;D. W. Stroock
  5. large deviations and statistical mechanics R. S. Ellis
  6. Ann. Prob. v.12 large deviations for a general class of dependent random vectors https://doi.org/10.1214/aop/1176993370
  7. Theory Probab. Appl. v.22 On large deviations from the invariant measure J. Gartner https://doi.org/10.1137/1122003
  8. Bull. Korean Math. Soc. v.32 On the rate function of convergence in large deviation probability D. Hwang
  9. Ph. D. thesis, OSU Large deviation principles for random measures
  10. Random measures O. Kallenberg
  11. Point processes and theory statistical A. F. Karr