Random transformations and invariance of semimartingales on Lie groups

Albeverio Sergio; De Vecchi Francesco C.; Morando PaolaUgolini Stefania

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Random transformations and invariance of semimartingales on Lie groups

机译：Random transformations and invariance of semimartingales on Lie groups

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摘要

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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来源
《Random operators and stochastic equations》 |2021年第1期|41-65|共25页
作者
Albeverio Sergio; De Vecchi Francesco C.; Morando PaolaUgolini Stefania;
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作者单位

Rheinische Friedrich Wilhelms Univ Bonn;

Univ Milan;

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正文语种英语
中图分类随机微分方程;
关键词
Semimartingale with jumps on Lie groups; stochastic processes on manifolds; invariance with respect to random transformations; stochastic characteristics of semimartingales; DIFFERENTIAL-EQUATIONS DRIVEN; INFINITELY DIVISIBLE MEASURES; LEVY PROCESSES; STOCHASTIC FLOWS; SYMMETRY GROUPS; ROUGH PATHS;

Random transformations and invariance of semimartingales on Lie groups

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