Summary
Let W(t) be a standard Wiener process and let L be the compact class figuring in Strassen's law of the iterated logarithm. We investigate the rate of convergence to zero of the variable
It is shown that as T→∞, (log log T)-α belongs to the upper class of this variable if α<2/3, and to the lower class if α>2/3.
References
Bolthausen, E.: On the speed of convergence in Strassen's law of the iterated logarithm. Ann. Probab. 6, 668–672 (1978)
Feller, W.: An introduction to probability theory and its applications 2. New York: Wiley 1966
Strassen, V.: An invariance principle for the law of iterated logarithm. Z. Wahrscheinlichkeitstheor. Verw. Geb. 3, 211–216 (1964)
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Grill, K. On the rate of convergence in Strassen's law of the iterated logarithm. Probab. Th. Rel. Fields 74, 583–589 (1987). https://doi.org/10.1007/BF00363517
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DOI: https://doi.org/10.1007/BF00363517
Keywords
- Stochastic Process
- Probability Theory
- Statistical Theory
- Wiener Process
- Lower Class