A General form of the Functional LIL for Banach-Valued Brownian Motion

Wong, H. Ship-Fah

Canadian journal of mathematics, Tome 36 (1984) no. 6, pp. 1046-1066

Résumé

In a recent paper [12], C. Mueller proved a general version of the functional LIL which unifies Strassen's LIL and the Lévy modulus of continuity for Brownian motion W(t). His theorem also contains other known forms of the LIL.For each t ≧ 0, let be a family of points in the first quadrant of the plane. Let r ≦ 0; to each point (s 0, l 0), we associate a rectangle Define Ar(t) to be the area of the union of these rectangles up to time t under the measure . Then, Theorem 1 [12, p. 166] states that for an increasing function h such that the set of limit points of in C[0, 1] is the closed unit ball of the reproducing kernel Hilbert space (rkhs) associated with Wiener measure.

Détail

DOI : 10.4153/CJM-1984-060-4

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