A note on the functional law of the iterated logarithm for Lévy's area process

Modeste N'zi, M'hamed Eddahbi
1997 Applicationes Mathematicae  
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process. This process has been thoroughly studied in recent years (see e.g. Ikeda, Kusuoka and Manabe [7] and Chan et al. [4] ) and plays an important role in the study of various problems in analysis, geometry, mathematical physics and statistics. For example, let B = {(B 1 (t), B 2 (t)) : t ≥ 0} be a 2dimensional Brownian motion and let ξ be the stationary Gaussian
more » ... onary Gaussian process 1991 Mathematics Subject Classification: 60F05, 60H05.
doi:10.4064/am-24-2-223-229 fatcat:6k4kblcjy5anlop6jlzaynqati