Symmetries of stochastic differential equations: A geometric approach

Journal Article · Wed Jun 15 04:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4953374· OSTI ID:22596854

Ugolini, Stefania ^[1]; Morando, Paola ^[2]

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1. Dipartimento di Matematica, Università degli Studi di Milano, via Saldini 50, Milano (Italy)
2. DISAA, Università degli Studi di Milano, via Celoria 2, Milano (Italy)

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.

• OSTI ID: 22596854
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 57; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BROWNIAN MOVEMENT
DIFFERENTIAL EQUATIONS
GEOMETRY
STOCHASTIC PROCESSES
SYMMETRY
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS