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Symmetry of stochastic equations

Giuseppe Gaeta
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Abstract

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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Giuseppe Gaeta. 2004-01-13. Symmetry of stochastic equations. https://arxiv.org/abs/math-ph/0401025

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