Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps

2017/08/05 by Sergio Albeverio, Albeverio, Sergio, Francesco C. De Vecchi +5
Economics, Econometrics and Finance · Mathematics · #58D19 #60G45 #60H10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1708.01764

openalex publication_date 2017/08/05 · openalex created_date 2017/08/17 · openalex updated_date 2026/07/28

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. In order to enlarge the class of possible symmetries of SDEs, the new concepts of gauge and time symmetries for semimartingales on Lie groups are introduced. Markovian and non-Markovian examples of gauge and time symmetric processes are provided. The considered set of SDEs includes affine and Marcus type SDEs as well as smooth SDEs driven by Lévy processes. Non trivial invariance results concerning a class of iterated random maps are obtained as special cases.

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• Random transformations and invariance of semimartingales on Lie groups
• Integration by parts formulas and Lie's symmetries of SDEs
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