Law of the iterated logarithm for the quadratic variation of a wiener process

LetP_a be the class of those partitions of intervals [,T], such that |t_i–t_i–1|>a, wherea is a constant,. It is proved that for anya lim V(T,P_a)/2Tln₂T=1 a. s., whereln_ix=ln ln x, ifln x e,ln₂x=1, ifln x <e.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 72–80, 1987.