Wiener's test for random walks with mean zero and finite variance
Uchiyama, K\^{o}hei
Ann. Probab., Tome 26 (1998) no. 1, p. 368-376 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
It is shown that an infinite subset of $Z^N$ is either recurrent for each aperiodic $N$-dimensional random walk with mean zero and finite variance, or transient for each of such random walks. This is an exact extension of the result by Spitzer in three dimensions to that in the dimensions $N \geq 4$.
Publié le : 1998-01-14
Classification:  Multidimensional random walk,  Green's function,  Laplace discrete operator,  Wiener's test,  Markov chain,  transient set,  60J15,  60J45,  31C20 
@article{1022855424,
     author = {Uchiyama, K\^{o}hei},
     title = {Wiener's test for random walks with mean zero and finite
 variance},
     journal = {Ann. Probab.},
     volume = {26},
     number = {1},
     year = {1998},
     pages = { 368-376},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022855424}
}

Uchiyama, K\^{o}hei. Wiener's test for random walks with mean zero and finite
 variance. Ann. Probab., Tome 26 (1998) no. 1, pp.  368-376. http://gdmltest.u-ga.fr/item/1022855424/