Summary
LetX t be a Brownian motion and letS(c) be the set of realsr≧0 such that üX r+t −X r ü≦c√t, 0≦t≦h, for someh=h(r)>0. It is known thatS(c) is empty ifc<1 and nonempty ifc>1, a.s. In this paper we prove thatS(1) is empty a.s.
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This research was partially supported by NSF Grant 9322689.