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. Morando
Penultimo
;
S. Ugolini
Ultimo
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.
Semimartingale with jumps on Lie groups, stochastic processes on manifolds, invariance with respect to random transformations, stochastic characteristics of semimartingales;
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/07 - Fisica Matematica
10-gen-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/810673
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