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.
Reduction and reconstruction of stochastic differential equations via symmetries / F.C. DE VECCHI, P. Morando, S. Ugolini. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 57:12(2016 Dec). [10.1063/1.4973197]
Reduction and reconstruction of stochastic differential equations via symmetries
F.C. DE VECCHIPrimo
;P. MorandoSecondo
;S. UgoliniUltimo
2016
Abstract
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.
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