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2020 Weak symmetries of stochastic differential equations driven by semimartingales with jumps
Sergio Albeverio, Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
Electron. J. Probab. 25: 1-34 (2020). DOI: 10.1214/20-EJP440

Abstract

Stochastic symmetries and related invariance properties of finite dimensional SDEs driven by general càdlàg semimartingales taking values in Lie groups are defined and investigated. The considered set of SDEs, first introduced by S. Cohen, includes affine and Marcus type SDEs as well as smooth SDEs driven by Lévy processes and iterated random maps. A natural extension to this general setting of reduction and reconstruction theory for symmetric SDEs is provided. Our theorems imply as special cases non trivial invariance results concerning a class of affine iterated random maps as well as (weak) symmetries for numerical schemes (of Euler and Milstein type) for Brownian motion driven SDEs.

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Sergio Albeverio. Francesco C. De Vecchi. Paola Morando. Stefania Ugolini. "Weak symmetries of stochastic differential equations driven by semimartingales with jumps." Electron. J. Probab. 25 1 - 34, 2020. https://doi.org/10.1214/20-EJP440

Information

Received: 26 April 2019; Accepted: 2 March 2020; Published: 2020
First available in Project Euclid: 4 April 2020

zbMATH: 07206382
MathSciNet: MR4089794
Digital Object Identifier: 10.1214/20-EJP440

Subjects:
Primary: 58D19, 60G45, 60H10

JOURNAL ARTICLE
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