2019/04/24 by Sergio Albeverio, Francesco C. De Vecchi, Paola Morando +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Affine transformation #Brownian motion #Euler's formula #Financial Risk and Volatility Modeling #Homogeneous space #Iterated function #Risk and Portfolio Optimization #Semimartingale #Stochastic differential equation #Stochastic processes and financial applications #Type (biology) #math-ph #math.MP #math.PR #msc:58D19 #msc:60G45 #msc:60H10
paper · pdf · doi:10.1214/20-ejp440
published as Electron. J. Probab., Volume 25 (2020), paper no. 44, 34 pp · arXiv admin note: substantial text overlap with arXiv:1708.01764
arxiv created 2019/04/24 · openalex created_date 2019/05/03 · openalex publication_date 2020/01/01 · arxiv updated 2020/08/04 · openalex updated_date 2026/08/05
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.