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An algorithmic method to exploit a general class of infinitesimal symmetriesfor reducing stochastic differential equations is presented and a naturaldefinition of reconstruction, inspired by the classical reconstruction byquadratures, is proposed. As a side result the well-known solution formula forlinear one-dimensional stochastic differential equations is obtained withinthis symmetry approach. The complete procedure is applied to several exampleswith both theoretical and applied relevance.

Reduction and reconstruction of stochastic differential equations via symmetries