zbMATH — the first resource for mathematics

Operators, stochastic processes, and Lie groups. (English) Zbl 0681.60014
Probability measures on groups IX, Proc. 9th Conf., Oberwolfach/FRG 1988, Lect. Notes Math. 1379, 75-85 (1989).
[For the entire collection see Zbl 0667.00022.]
The construction of processes on Lie groups corresponding to processes on \({\mathbb{R}}^ n\) via exponential mapping is discussed. This fits in with the operator approach to stochastic processes in the author’s article reviewed above, see the preceding review, Zbl 0681.60013. Probability limit theorems on Lie groups used in construction of the processes concurrently establish the existence of certain multiple stochastic integrals of the \({\mathbb{R}}^ n\)-valued processes. Various examples of processes, e.g. on nilpotent and solvable groups, are presented.
Reviewer: Ph.Feinsilver

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization