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Let Y74X-1&_mathId=mml2&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=ff75180737898f0357548e9b5a6727a2""> be a one-dimensional fractional Brownian motion with Hurst parameter yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml3&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=c7ef61e7b39983baad4d7381e3374f29"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">H(0,1). We study the functionals

We show that there exists a constant yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml5&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=6e173be6595ba2ab97ca7eaa148fb2a3"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">pH(1,2) depending only on yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml6&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=5d3ca3ce9f6dd017ad0aa802d6b1b436"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">H such that the yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml7&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=407e5c6e739f74048c9606251aa31158"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">p-variation of (yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml9&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=65795eb99099b36fb83fe544716d4f2c"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">j=1,2) is zero if yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml10&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=fd6a986b1059b7ea6aa4d30de581b4e1"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">p>pH, where yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml11&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=600bb0da1571e03bededd62ba82373a0"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">L1,L2 are the local time and weighted local time of yle=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1D-4R9Y74X-1&_mathId=mml12&_user=1067359&_cdi=5672&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=36d73271881a828de16b5e62369199c7"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">BH, respectively. This extends the illustrated result for Brownian motion.

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