2016/07/28 by Francesco C. De Vecchi, Paola Morando, Stefania Ugolini · 4 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Class (philosophy) #Computer science #Differential equation #Geometry #Homogeneous space #Infinitesimal #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematics #Numerical partial differential equations #Reduction (mathematics) #Statistical Mechanics and Entropy #Stochastic differential equation #Stochastic partial differential equation #Stochastic processes and financial applications #math-ph #math.MP #math.PR #msc:58D19 #msc:60H10
paper · pdf · doi:10.1063/1.4973197
published as Journal of Mathematical Physics 57, 123508 (2016)
arxiv created 2016/07/28 · openalex publication_date 2016/12/01 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.