Compound Poisson processes and Lévy processes in groups and symmetric spaces (Q1582128)

The paper deals with three themes. The first is the description of the paths of Lévy processes in groups. The author shows that the paths of a Lévy process in a (locally compact Hausdorff) group can be obtained as the almost sure limit of a sequence of Brownian motions interlaced with random jumps. The second theme is the characterisation of Lévy processes in Riemannian globally symmetric spaces. Results of \textit{R. Gangolli} [Pac. J. Math. 15, 477---496 (1965; Zbl 0141.14903)] are generalised and a simpler proof of Gangolli's Lévy-Khinchin formula is given. Finally, the third theme is constructing Fock space realisations for spherically symmetric Lévy processes in groups and factorizable representations of current groups.