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2 Journal of Applied Analysis

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Probability on matrix-cone hypergroups: limit theorems and structural properties

Hazod W.

Journal of Applied Analysis

2009

Vol. 15, nr 2

205-245

Recent investigations of M. Rösler [13] and M. Voit [17] provide examples of hypergroups with properties similar to the group-or vector space case and with a sufficiently rich structure of automorphisms, providing thus tools to investigate the limit theory of normalized random walks and the structure of the corresponding limit, laws. The investigations are parallel to corresponding investigations for vector spaces and simply connected nilpotent Lie groups.

Semistable selfdecomposable laws on groups

Hazod W., Shah R.

Journal of Applied Analysis

2001

Vol. 7, nr 1

1-22

The most prominent examples of (operator-) selfdecomposable laws on vector spaces are (operator-) stable laws. In the past (operator-) semistability — a natural generalisation — had been intensively investigated, hence the description of the intersection of the classes of semistable and selfdecomposable laws turned out to be a challenging problem, which was finally solved by A. Łuczak's investigations [17]. For probabilities on groups, in particular on simply connected nilpotent Lie groups there exists meanwhile a satisfying theory of decomposability and semistability. Consequently it is possible to obtain a description of the intersection of these classes of measures — under additional commutativity assumptions — leading finally to partial extensions of the above-mentioned results for vector spaces to the group case.