Exponentials and $R$-recurrent random walks on groups

M. G. Shur

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arXiv · 1511.02810

Exponentials and $R$-recurrent random walks on groups

M. G. Shur

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Abstract

On a locally compact group $E$ with countable base, we consider a random walk $X$ that has a unique (up to a positive factor) $r$-invariant measure for some $r>0$. Under some weak conditions on the measure, there is a unique continuous exponential on $E$ naturally associated with $X$. It follows that there exists an $R$-recurrent random walk in the sense of Tweedie on $E$ if and only if $E$ is a recurrent group and there exists a Harris random walk on~$E$.

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BibTeX RIS

M. G. Shur. 2015-11-09. Exponentials and $R$-recurrent random walks on groups. https://arxiv.org/abs/1511.02810

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