Summary
Let {K(s,t): 0≦s≦1, t≧0} be a Kiefer process. Let
denote the occupation distribution. Using the ideas of Mogul'skii, Donsker and Varadhan, the limit behavior of L t is studied. These and strong approximation results are then used to derive LIL in Chung's form for various functions of empirical processes.
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References
Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Wiener integrals for large time. In Functional Integration and Its Applications. Proceedings of the International converence, London, 15–33. Oxford: Clarendon Press 1975
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This work was done while the author was visiting the Department of Mathematics, University of Ottawa, Ottawa, Canada
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Babu, G.J. On the law of iterated logarithm for occupation measures of empirical processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 73–81 (1983). https://doi.org/10.1007/BF00534995
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DOI: https://doi.org/10.1007/BF00534995