Functional central limit theorems for locally compact groups: The use of infinite dimensional Fourier analysis (Q2751512)

Let \(G\) be a second countable locally compact group and \(\{X_{nl}; n,l\in N\}\) an infinitesimal array of rowwise independent \(G\)-valued random variables. The problem is to find conditions that ensure weak convergence of \(X_n(t)= \prod^{k_n(t)}_{l=1} X_{nl}\) to an increment process \(X(t)\). The present article aims at surveying the methodical tools and some recent results achieved to solve this problem. In particular, using the infinite-dimensional Fourier analysis the author elaborates on an axiomatic approach to Lévy continuity property which plays an important role in arriving at desired functional central limit theorems. This clearly written survey may be viewed as a supplement actualizing the previous one by \textit{Pap} [7th Internat. Vilnius Conf. Probab. Theory and Math. Stat. and 22nd EMS Proc., Vilnius (1998)].NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].