Symmetries of stochastic differential equations: A geometric approach

被引：15
|
作者：
De Vecchi, Francesco C. [1 ]
Morando, Paola [2 ]
Ugolini, Stefania [1 ]
机构：
[1] Univ Milan, Dipartimento Matemat, Via Saldini 50, Milan, Italy
[2] Univ Milan, DISAA, Via Celoria 2, Milan, Italy
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2016年 / 57卷 / 06期
关键词：
LIE-POINT SYMMETRIES;
D O I：
10.1063/1.4953374
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion. Published by AIP Publishing.
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页数：17
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