Construction of processes with stationary independent increments in Lie groups
type: Item
instance of: scholarly article
title: Construction of processes with stationary independent increments in Lie groups
zbMATH Open document ID: 0904.60008
author: Gyula Pap
published in: Archiv der Mathematik
publication date: 1998-07-13T00:00:00Z
review text: Lévy processes on exponential Lie groups are described as unique solutions of stochastic differential equations where these SDEs are given in terms of the generators of the associated convolution semigroups. This result is stated not for the Lévy process on the exponential Lie group but rather for the associated process on the Lie algebra. The proof is based on the well-posedness of some martingale problem due to Ph. Feinsilver. Closely related characterizations for functionals fo Lévy processes were recently derived by \textit{D. Applebaum} and \textit{H. Kunita} [J. Math. Kyoto Univ. 33, No. 4, 1103-1123 (1993; Zbl 0804.58057)]. In the end of this note, the main result is applied to simply connected nilpotent Lie groups in which case an inductive explicit description of Lévy processes is given.
reviewed by: Michael Voit
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 1145406
zbMATH Keywords: Lévy processes
zbMATH Keywords: Lie groups
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: martingale problem
Wikidata QID: Q115390143
MaRDI profile type: Publication
full work available at URL: s000130050104
OpenAlex ID: W1982990415
DOI: 10.1007/S000130050104
description: scientific article; zbMATH DE number 1145406