关于Wiener过程泛函连续模的精确收敛速度

设{W（t）,t≥0}是一标准Wiener过程,记S是Strassen重对数律的紧集类·本文中我们讨论了两个变量sup_0≤t≤1-h inf_f∈S sup_0≤x≤1 |(W(t+hx)-W(t))(2h log h^-1)^-1/2 - f(x)|及inf_0≤t≤1-h sup_0≤x≤1 |(W(t + hx) - W(t))(2hlogh^-1)^-1/2- f(x)|（对任何f∈S）趋于零的精确的收敛速度.作为一个推广,我们建立了Wiener过程的不可微模与泛函的连续模之间的一种关系.

Exact Convergence Rates of Functional Modulus of Continuity of a Wiener Process

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 snP0＜t＜1-h inff∈S suP0＜x＜1 |(W(t + hx) - W(t))(2h log h-1)-1/2 - f(x)| andinfo＜t＜1-h supo≤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.