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

关于Wiener过程泛函连续模的精确收敛速度(英文)

Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-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 a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.

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sup0≤t≤1-hinff∈Ssup0≤x≤1|（W（t +hx）-W（t））（2hlogh-1）-1/2-f（x）|及inf0≤t≤1-hsup0≤x≤1|（W（t+hx）-W（t））（2hlogh-1）-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.