A critical case for Brownian slow points

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A critical case for Brownian slow points

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Title: A critical case for Brownian slow points
Author: Burdzy, Krzysztof; Bass, Richard F.
Abstract: Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less than or equal to] t [is less than or equal to] h, for some h = h(r) > 0. It is known that S(c) is empty if c < 1 and nonempty if c > 1, a.s. In this paper we prove that S(1) is empty a.s.
URI: http://hdl.handle.net/1773/2191

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