Escape probabilities for slowly recurrent sets
Escape probabilities for slowly recurrent sets
复制标题
缓慢循环集的逃逸概率
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
G. Lawler
中科院分区：
文献类型：
--
作者：
G. Lawler
设一个简单随机游动的集合A <$Zd（d>-3）是慢常返的，如果它是常返的，但进入A <${z：n<|z| <-2n}趋于零，as n →∞。给出了一种方法来估计这种集合的逃逸概率，即，离开半径球而不进入集合的概率。该方法被应用到两个例子。首先，考虑Z3中的半直线和半直线的有限并。第二个例子是一个四维的随机行走路径。在后一种情况下，证明了两条随机游动路径到达半径球n而不相交的概率是渐近的toc（lnn）−1/2，改进了作者的一个结果.
SummaryA setA⊂Zd (d>-3) is defined to be slowly recurrent for simple random walk if it is recurrent but the probability of enteringA∩{z:n<|z|<-2n} tends to zero asn→∞. A method is given to estimate escape probabilities for such sets, i.e., the probability of leaving the ball of radiusn without entering the set. The methods are applied to two examples. First, half-lines and finite unions of half-lines inZ3 are considered. The second example is a random walk path in four dimensions. In the latter case it is proved that the probability that two random walk paths reach the ball of radiusn without intersecting is asymptotic toc(lnn)−1/2, improving a result of the author.