2004/01/13 by Giuseppe Gaeta
Physics and Astronomy · Mathematics · #math-ph #math.MP
published as Proc. Nat. Acad. Sci. Ukraine 50 (2004), 98-109 · Work prepared for the Kyev SNMP2003 conference proceedings
arxiv created 2004/01/13 · arxiv updated 2009/12/01
Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry considerations are of course quite widely used by theoretical physicists, but a rigorous and general theory comparable to the one developed for deterministic equation is still lacking. In the following I will report on some work I have done on symmetries of stochastic (Ito) equations, and how these compare with the symmetries of the associated diffusion (Fokker-Planck) equations.