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.
Random transformations and invariance of semimartingales on Lie groups / S. Albeverio, F.C. De Vecchi, P. Morando, S. Ugolini. - In: RANDOM OPERATORS AND STOCHASTIC EQUATIONS. - ISSN 0926-6364. - 29:1(2021 Mar), pp. 000010151520202052.41-000010151520202052.65. [10.1515/rose-2020-2052]
Random transformations and invariance of semimartingales on Lie groups
P. MorandoPenultimo
;S. UgoliniUltimo
2021
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.
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