# 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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