Reduction and reconstruction of stochastic differential equations via   symmetries
  An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance. 
Francesco C. De Vecchi, Paola Morando, Stefania Ugolini
math.PR math-ph math.MP