The minimal subgroup of a random walk (Q1610501)

The author proves that for each random walk \((S_{n})\) on \(\mathbb R^{d}\) there exists a minimal subgroup \(G\) such that \(P(S_{n}\in G)=1\), \(\forall n\geq 1\). The minimal subgroup of the symmetrization of \((S_{n})\) is also considered. Finally, the quasi-invariance and the admissible shift of probability measures on \(\mathbb R^{d}\) are studied.