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.
Symmetries of stochastic differential equations : a geometric approach / F.C. De Vecchi, P. Morando, S. Ugolini. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 57:6(2016 Jun 10), pp. 063504.1-063504.17. [10.1063/1.4953374]
Symmetries of stochastic differential equations : a geometric approach
F.C. De VecchiPrimo
;P. MorandoSecondo
;S. UgoliniUltimo
2016
Abstract
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.
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