The increments of a bifractional Brownian motion
2009 ◽
Vol 46
(4)
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pp. 449-478
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Let { BH;K ( t ), t ≧ 0} be a bifractional Brownian motion with indexes 0 < H < 1 and 0 < K ≦ 1 and define the statistic \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$V_T = \mathop {\sup }\limits_{0 \leqq s \leqq T - a_T } \beta _T \left| {B_{H,K} (s + a_T ) - B_{H,K} (s)} \right|$$ \end{document} where βT and αT are suitably chosen functions of T ≧ 0. We establish some laws of the iterated logarithm for VT .
1995 ◽
Vol 8
(3)
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pp. 643-667
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2013 ◽
Vol 50
(1)
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pp. 67-121
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2020 ◽
Vol 12
(1)
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pp. 128-145
2011 ◽
Vol 26
(2)
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pp. 127-141
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2010 ◽
Vol 53
(11)
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pp. 2973-2992
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