Points of increase for random walks

被引：6
|
作者：
Peres, Y [1 ]
机构：
[1] UNIV CALIF BERKELEY,DEPT STAT,BERKELEY,CA 94720
来源：
ISRAEL JOURNAL OF MATHEMATICS | 1996年 / 95卷
关键词：
D O I：
10.1007/BF02761045
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Say that a sequence S-0,...,S-n has a (global) point of increase at k if S-k is maximal among S-0,...,S-k and minimal among S-k,...S-n. We give an elementary proof that an n-step symmetric random walk on the line has a (global) point of increase with probability comparable to 1/log n. (No moment assumptions are needed.) This implies the classical fact, due to Dvoretzky, Erdos and Kakutani (1961), that Brownian motion has no points of increase.
引用
收藏
页码：341 / 347
页数：7
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