Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process
Received:September 14, 1999  
Key Words: Wiener process   functional modulus of continuity   modulus of non-differentiability  
Fund Project:Supported by NNSFC (10071072) and Science Foundation of Hangzhou Teacher'sCollege.
Author NameAffiliation
WANG Wen-sheng Dept. of Math.
Hangzhou Teacher's College
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      Let {W(t),t ≥ 0} be a standard Wiener process and S be the set of Strassen'sfunctions. In this paper we investigate the exact rates of convergence to zero of thevariables sup0≤t≤1-h inff∈S sup0≤x≤1 |(W(t+hx)-W(t))(2h log h-1)-1/2 - f(x)| and inf0≤t≤1-h sup0≤x≤1 |(W(t + hx) - W(t))(2hlogh-1)-1/2- f(x)| for any f ∈ S. As aconsequence, a relation between the modulus of non-differentiability and the fiunctionalmodulus of continuity for a Wiener process is established.
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