Geodesic
Exponentials and $R$-recurrent random walks on groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 580-588 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Babillot M., “An introduction to Poisson boundaries of Lie groups”, Probability Measures on Groups: Recent Directions and Trends, eds. S. G. Dany, P. Graczyk, Narosa Publ. House, New Delhi, 2006, 1–90 | MR | Zbl

[2] Baldi P., “Caractérization des groupes de Lie connexes récurrents”, Ann. Inst. Henri Poincaré, Probab. Satist., 17 (1981), 281–308 | MR | Zbl

[3] Guivarc'h Y., Keane M., Roynette B., Marches aléatoiries sur les groupes de Lie, Lecture Notes in Math., 624, 1977, 292 pp. | DOI | MR

[4] Nummelin E., General Irreducible Markov Chains and Non-negative Operators, Cambridge Univ. Press, Cambridge, 1984, 156 pp. | MR | Zbl

[5] Tweedie R. L., “Theory for Markov chains on a general state space. I; II”, Ann. Probab., 2 (1974), 840–864 ; 865–878 | DOI | MR | Zbl | MR | Zbl

[6] Woess W., Random Walks on Infinitife Graphs and Groups, Cambridge Univ. Press, Cambridge, 2000, 334 pp. | MR

[7] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, v. 1, Nauka, M., 1975, 654 pp.

[8] Revyuz D., Tsepi Markova, RFFI, M., 1997, 431 pp.

[9] Shur M. G., “Uslovie ravnomernoi integriruemosti v silnykh predelnykh teoremakh dlya otnoshenii, III”, Teoriya veroyatn. i ee primen., 57:4 (2012), 682–700 | DOI