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. A43 (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. Phys.58 (2017)].
Symmetry and integrability for stochastic differential equations / G. Gaeta, C. Lunini. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 25:2(2018 Apr), pp. 262-289. [10.1080/14029251.2018.1452673]
Symmetry and integrability for stochastic differential equations
G. GaetaPrimo
;
2018
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. A43 (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. Phys.58 (2017)].
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