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
De Vecchi F. C.;
2021-01-01
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.File in questo prodotto:
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