WEAK CONVERGENCE TO BROWNIAN MOTION

作     者：Thomas B.Paine Department of Mathematics Southern Illinois University Carbondale,IL 62901-4408 

出 版 物：《东北师大学报(自然科学版)》 (Journal of Northeast Normal University(Natural Science Edition))

年 卷 期：1990年第2期

页      面：1-17页

核心收录：

主　　题：Brownian motion weak convergence 

摘      要：Let X;=(X;（t）: t≥0) denote the continuous polygonalfunction whose vertices are where s;=z;+…+z;and the Z;’s are independent random variables with Ez;=0,vat z;=σ;;v;=σ;+…+σ;.Under standard condition onexpected values of ,itis shown that Xm converges weakly to Brownian motion in thetopology induced by the metric ρ（x,y） =wherex and y denote real continuous functions on [0,∞) and t log log tis taken to be 1 when t≤e;.A comparison is made withSakhanenkos’ similar *** is also shown thatconvergence,in probability,of the Skorokhod embedding times isa necessary condition for weak convergence to Brownian motion onthe unit interval under the supremum norm