Stochastic symmetries and related invariance properties of ﬁnite dimensional SDEs driven by general c`adl`ag 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 L´evy 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.
Weak symmetries of stochastic differential equations driven by semimartingales with jumps / S. Albeverio, F.C. De Vecchi, P. Morando, S. Ugolini. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 25(2020), pp. 44.1-44.34.
|Titolo:||Weak symmetries of stochastic differential equations driven by semimartingales with jumps|
MORANDO, PAOLA (Penultimo)
UGOLINI, STEFANIA (Ultimo)
|Parole Chiave:||Lie symmetry analysis; stochastic diﬀerential equations; semimartingales with jumps; stochastic processes on manifolds|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
Settore MAT/07 - Fisica Matematica
|Data di pubblicazione:||2020|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1214/20-EJP440|
|Appare nelle tipologie:||01 - Articolo su periodico|