Symmetry and integrability for stochastic differential equations

@article{Gaeta2017SymmetryAI,
  title={Symmetry and integrability for stochastic differential equations},
  author={Giuseppe Gaeta and Claudia Lunini},
  journal={Journal of Nonlinear Mathematical Physics},
  year={2017},
  volume={25},
  pages={262 - 289}
}
  • G. Gaeta, C. Lunini
  • Published 17 November 2017
  • Mathematics
  • Journal of Nonlinear Mathematical Physics
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. Phys. 58 (2017)]. 
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