Rates of convergence for the functional LIL
Let \(X,X_ 1,X_ 2,..\). be i.i.d. random variables such that E X\(=0\), E \(X^ 2=1\). Let S(t), \(t\geq 0\), be the polygonal process. The rate of convergence of the random sequence \[ \{S(n(\cdot))/(2n LL n)^{1/2},\quad n\geq 1\} \] to a compact convex symmetric subset of C[0,1] is obtained. Under additional assumptions, the same result has earlier been proved by the authors in J. Theor. Probab. 1, 27-63 (1988; Zbl 0651.60039).
scientific article; zbMATH DE number 4100268