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Symmetry of stochastic non-variational differential equations. (English) Zbl 1366.34083
Phys. Rep. 686, 1-62 (2017); erratum ibid. 713, 18 (2017).
Summary: I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more and less recent attempts to extend this theory to the study of stochastic differential equations, and briefly mention some perspective in this direction.

MSC:
34F05 Ordinary differential equations and systems with randomness
34K50 Stochastic functional-differential equations
35R60 PDEs with randomness, stochastic partial differential equations
Software:
MACSYMA; SYMMGRP
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References:
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