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2018•Journal of Nonlinear Mathematical PhysicsOpen access

Symmetry and integrability for stochastic differential equations

Giuseppe Gaeta, Claudia Lunini

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Abstract

We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J.Phys.A 43 (2010) & 44 (2011)].Together with integrability, we also consider the relations between symmetries and reducibility of a system of SDEs to a lower dimensional one.We consider both "deterministic" symmetries and "random" ones, in the sense introduced recently by Gaeta and Spadaro [J.Math.

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We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J.Phys.A 43 (2010) & 44 (2011)].Together with integrability, we also consider the relations between symmetries and reducibility of a system of SDEs to a lower dimensional one.We consider both "deterministic" symmetries and "random" ones, in the sense introduced recently by Gaeta and Spadaro [J.Math.

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Available abstract

We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J.Phys.A 43 (2010) & 44 (2011)].Together with integrability, we also consider the relations between symmetries and reducibility of a system of SDEs to a lower dimensional one.We consider both "deterministic" symmetries and "random" ones, in the sense introduced recently by Gaeta and Spadaro [J.Math.

Key concepts: Homogeneous space, Symmetry (geometry), Stochastic differential equation, Mathematics, Mathematical physics, Pure mathematics, Differential equation, Mathematical analysis

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