Convergence of evolution operator families and its applications to functional limit theorems (Q2714383)

This paper is part of a recent series of papers of the authors on triangular central limit theorems and convolution hemigroups on locally compact groups. In the present paper, the authors investigate the convergence of triangular systems of probability measures and of the associated random walks on an arbitrary locally compact group \(G\). Sufficient conditions are given in terms of irreducible unitary representations such that the random walks on \(G\) converge to a càdlàg process on \(G\) with independent increments. Depending on the validity of Lévy's continuity theorem for \(G\), the limit process has to be specified here. The proof uses some Fourier analysis and informations about convolution hemigroups whose Fourier images are of finite variation.