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On the rate of convergence in Strassen's law of the iterated logarithm

✍ Scribed by Karl Grill

Publisher
Springer
Year
1987
Tongue
English
Weight
198 KB
Volume
74
Category
Article
ISSN
1432-2064

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✦ Synopsis

Let W(t) be a standard Wiener process and let 5 p 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~oo, (loglog T) -~ belongs to the upper class of this variable if e<~, and to the lower class if c~> 2.

πŸ“œ SIMILAR VOLUMES

Strassen's local law of the iterated log
Strassen's local law of the iterated logarithm for LΓ©vy's area
✍ Modeste N'Zi πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 288 KB

We prove a Strassen's law of the iterated logarithm at zero for L&y's area process. Contrary to the Brownian case, the time inversion argument doesn't seem to work. Here, the main tool in the proof is large deviations estimates for diffusion processes with small diffusion coefficients. Loi locale