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.
References
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)
Cameron, R.H., Martin, W.T.: The transformation of Wiener integrals by nonlinear transformations. Trans. Am. Math. Soc.75, 552–575 (1953)
Chung, K.L.: On the maximum partial sums of sequences of independent random variables. Trans. Am. Math. Soc.64, 205–233 (1948)
Csáki, E.: A relation between Chung's and Strassen's laws of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.54, 287–301 (1980)
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
Donsker, M.D., Varadhan, S.R.S.: On laws of the iterated logarithm for local times. Commun. Pure Appl. Math.30, 707–753 (1977)
Ito, K., McKean, Jr., H.P.: Diffusion processes and their sample paths. Berlin Heidelberg New York: Springer 1965
Kesten, H.: An iterated logarithm law for local time. Duke Math. J.32, 447–456 (1965)
McKean, Jr., H.P.: Stochastic integrals. New York London: Academic Press 1969
Mueller, C.: Strassen's law for local time. Z. Wahrscheinlichkeitstheor. Verw. Geb.63, 29–41 (1983)
Strassen, V.: An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb.3, 227–246 (1964)
Wichura, M.: Unpublished
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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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DOI: https://doi.org/10.1007/BF01312216
Keywords
- Stochastic Process
- Brownian Motion
- Probability Theory
- Mathematical Biology
- Iterate Logarithm