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SUMMARY:Unbiased shifts of Brownian Motion - Thorisson\, H (University of 
 Iceland)
DTSTART:20130816T133000Z
DTEND:20130816T141500Z
UID:TALK46666@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let $B = (B_t)_{tinmathbb{R}}$ be a two-sided standard Brownia
 n motion. Let $T$ be a measurable function of $B$. Call $T$ an mph{unbias
 ed shift} if $(B_{T+t}-B_T)_{tinmathbb{R}}$ is a Brownian motion independe
 nt of $B_T$. We characterize unbiased shifts in terms of allocation rules 
 balancing local times of $B$. For any probability distribution $\nu$ on $m
 athbb{R}$ we construct a nonnegative stopping time $T$ with the above prop
 erties such that $B_T$ has distribution $\nu$. In particular\, we show tha
 t if we travel in time according to the clock of local time at zero we alw
 ays see a two-sided Brownian motion. A crucial ingredient of our approach 
 is a new theorem on the existence of allocation rules balancing jointly st
 ationary diffuse random measures on $mathbb{R}$. We also study moment and 
 minimality properties of unbiased shifts.\n
LOCATION:Seminar Room 1\, Newton Institute
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