Summary
LetW(t) be a Wiener process. The lim inf behavior of theL 2-norm ofW(t) on the interval [T-a(T), T] and of |W(t+θT)−W(t)| on the interval [αT, βT] is given under suitable conditions.
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Supported in part by NSF grant number DMS-8521586 and DMS-9024961
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Li, W.V. Lim inf results for the Wiener process and its increments under theL 2-norm. Probab. Th. Rel. Fields 92, 69–90 (1992). https://doi.org/10.1007/BF01205237
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DOI: https://doi.org/10.1007/BF01205237