Geodesic
On A Brownian Motion Problem of T. Salisbury
Canadian mathematical bulletin, Tome 40 (1997) no. 1, pp. 67-71

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Let B be a Brownian motion on R, B(0) = 0, and let f (t, x) be continuous. T. Salisbury conjectured that if the total variation of f (t, B(t)), 0 ≤ t ≤ 1, is finite P-a.s., then f does not depend on x. Here we prove that this is true if the expected total variation is finite.
DOI : 10.4153/CMB-1997-008-x
Mots-clés : 60J65 
Knight, Frank B. On A Brownian Motion Problem of T. Salisbury. Canadian mathematical bulletin, Tome 40 (1997) no. 1, pp. 67-71. doi: 10.4153/CMB-1997-008-x
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     title = {On {A} {Brownian} {Motion} {Problem} of {T.} {Salisbury}},
     journal = {Canadian mathematical bulletin},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-008-x/}
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