Abstract
Let X t be the Levy symmetric stable process with index α ∈ [1, 2), and let C be a convex, symmetric subset of L α [0, 1]. We prove that if C does not have compact closure then sup ƒϵC ¦∝ 0 1ƒ(t)dX t¦ is infinite with probability one. This extends a result of Dudley in the case α = 2.
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