Symmetries of stochastic differential equations using Girsanov transformations

@article{DeVecchi2020SymmetriesOS,
  title={Symmetries of stochastic differential equations using Girsanov transformations},
  author={Francesco C. De Vecchi and Paola Morando and Stefania Ugolini},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={53}
}
Aiming at enlarging the class of symmetries of a stochastic differential equation (SDE), we introduce a family of stochastic transformations able to change also the underlying probability measure exploiting Girsanov theorem and we provide new determining equations for the infinitesimal symmetries of the SDE. The well-defined subset of the previous class of measure transformations given by Doob transformations allows us to recover all the Lie point symmetries of the Kolmogorov equation… 

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