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

Published online by Cambridge University Press:  20 November 2018

H. Ship-Fah Wong
H. Ship-Fah Wong*
Affiliation:
University of Ottawa, Ottawa, Ontario
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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 (s0, l0), 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 36 , Issue 6 , 01 December 1984 , pp. 1046 - 1066
Copyright
Copyright © Canadian Mathematical Society 1984

References

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