Symmetry of stochastic equations

Details Symmetry of stochastic equations Symmetry of stochastic equations

2004-01-13

arxiv.org/abs/math-ph/0401025v1

Proc. Nat. Acad. Sci. Ukraine 50 (2004), 98-109

Physics

Mathematical Physics

Work prepared for the Kyev SNMP2003 conference proceedings

Scientific paper

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.

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