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A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm
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  • Published: September 1991

A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm

  • Carl Mueller1 

Probability Theory and Related Fields volume 87, pages 365–388 (1991)Cite this article

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  • 2 Citations

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Summary

A connection is given between various functional laws of the iterated logarithm for Brownian motion due to Donsker and Varadhan, Csáki, Chung, Strassen, and the author.

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References

  1. Acosta, A. De: Small deviation in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab.11, 78–101 (1983)

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  3. Chung, K.L.: On the maximum partial sums of sequences of independent random variables. Trans. Am. Math. Soc.64, 205–233 (1948)

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  4. Csáki, E.: A relation between Chung's and Strassen's laws of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.54, 287–301 (1980)

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  5. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Wiener integrals for large time. In: Functional integration and its applications, pp. 15–33. Proceedings of the International Congress, London. Oxford: Clarendon Press 1975

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  9. McKean, Jr., H.P.: Stochastic integrals. New York London: Academic Press 1969

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  10. Mueller, C.: Strassen's law for local time. Z. Wahrscheinlichkeitstheor. Verw. Geb.63, 29–41 (1983)

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  11. Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 227–246 (1964)

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  12. Wichura, M.: Unpublished

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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, Ray P. Hylan Building, 14627, Rochester, NY, USA

    Carl Mueller

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  1. Carl Mueller
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Supported by an NSF grant

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Cite this article

Mueller, C. A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm. Probab. Th. Rel. Fields 87, 365–388 (1991). https://doi.org/10.1007/BF01312216

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  • Received: 24 November 1988

  • Revised: 01 June 1990

  • Issue Date: September 1991

  • DOI: https://doi.org/10.1007/BF01312216

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Iterate Logarithm
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