Geodesic
Exponentials and $R$-recurrent random walks on groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 580-588

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On a locally compact group $E$ with a countable base we consider a right random walk $X$ which for some $r>0$ has a unique (up to a positive multiplier) $r$-invariant measure. If this measure obeys some weak restrictions, then the random walk $X$ corresponds to the single continuous exponential on $E$. From this we obtain that we can implement some $R$-recurrent (by Tweedie) random walk on the group $E$ only in the case when this group is recurrent and, moreover, when there exists a Harris recurrent random walk on it.
Keywords: $r$-invariant measure, $R$-recurrent walk on a group, random walk, Harris recurrent walk, exponential. 
@article{TVP_2016_61_3_a8,
     author = {M. G. Shur},
     title = {Exponentials and $R$-recurrent random walks on groups},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {580--588},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a8/}
}
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M. G. Shur. Exponentials and $R$-recurrent random walks on groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 580-588. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a8/