Recurrence of Co-Cycles and Random Walks
Recurrence of Co-Cycles and Random Walks
复制标题
共循环和随机游走的重现
DOI：
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发表时间：
1976
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影响因子：
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通讯作者：
G. Atkinson
中科院分区：
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作者：
G. Atkinson
P{A n T~A)n{x：AF(n，x)<；e})>；0.不循环的共周期称为暂时性的。Schmidt在[1]中分析了一般局部紧交换群的斜积扩张的结构。证明了上循环Af是常返的当且仅当相应的扩张Sf是保守的(定理4.3)。由U上的概率测度A定义的U上的随机游动可以用如下方式实现为斜积扩张：设X是空间Yl^ji=-oo(每个Ut=U)，具有乘积Borel结构；令ji是每个因子中与X相同的测度的乘积；令T是移位
p{A n T~A) n {x: af(n, x) < e}) > 0. Co-cycles which are not recurrent are called transient. The structure of skew-product extensions into general locally compact abelian groups has been analysed by Schmidt in [1]. It is shown there that a co-cycle af is recurrent if and only if the corresponding extension Sf is conservative (Theorem 4.3). A random walk on U, which is defined by a probability measure A on U, may be oo realised as a skew-product extension in the following way: let X be the space Yl ^j i = — oo (each Ut = U), with the product Borel structure; let ji be the product of measures identical to X in each factor; let T be the shift