Random transformations and invariance of semimartingales on Lie groups-Reference-Cited by-同舟云学术

Random transformations and invariance of semimartingales on Lie groups

Published:2021-01-20 Issue:1 Volume:29 Page:41-65
ISSN:1569-397X
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Albeverio Sergio¹,De Vecchi Francesco C.¹^ORCID,Morando Paola²,Ugolini Stefania³

Affiliation:

1. Institut für Angewandte Mathematik and HCM , Rheinische Friedrich-Wilhelms-Universität Bonn , Endenicher Allee 60 , Bonn , Germany

2. DISAA , Università degli Studi di Milano , via Celoria 2 , Milano , Italy

3. Dipartimento di Matematica , Università degli Studi di Milano , via Saldini 50 , Milano , Italy

Abstract

Abstract Invariance properties of semimartingales on Lie groups under a family of random transformations are defined and investigated, generalizing the random rotations of the Brownian motion. A necessary and sufficient explicit condition characterizing semimartingales with this kind of invariance is given in terms of their stochastic characteristics. Non-trivial examples of symmetric semimartingales are provided and applications of this concept to stochastic analysis are discussed.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2020-2052/pdf

Reference53 articles.

1. S. Albeverio, A. B. Cruzeiro and D. Holm, Stochastic Geometric Mechanics, Springer Proc. Math. Stat. 202, Springer, Cham, 2017.

2. S. Albeverio, F. C. De Vecchi, P. Morando and S. Ugolini, Weak symmetries of stochastic differential equations driven by semimartingales with jumps, Electron. J. Probab. 25 (2020), Paper No. 44.

3. S. Albeverio and S.-M. Fei, Symmetry, integrable chain models and stochastic processes, Rev. Math. Phys. 10 (1998), no. 6, 723–750.

4. S. Albeverio and M. Gordina, Lévy processes and their subordination in matrix Lie groups, Bull. Sci. Math. 131 (2007), no. 8, 738–760.

5. D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd ed., Cambridge Stud. Adv. Math. 116, Cambridge University, Cambridge, 2009.

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