Symmetry of stochastic non-variational differential equations

Abstract

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.

arXiv commentReview paper (119 pages) here in bookstyle. The published version may differ from the present (preprint) one. Version 2 (November 2017): due to a mistake in a basic formula (in a previous paper of mine) the content of Section 5.5 gives wrong statement; an ERRATUM has been added at the end of the file; see also arXiv:1711.01999 for correct results on that topic

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Cited by in corpus (14)

• Symmetry of stochastic non-variational differential equations
• W-Symmetries of Ito stochastic differential equations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
• Noether theorem in stochastic optimal control problems via contact symmetries
• Integration of the stochastic logistic equation via symmetry analysis
• Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps
• Integrable Ito equations and properties of the associated Fokker-Planck equations
• Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
• Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
• Recent advances in symmetry of stochastic differential equations
• On the integration of Ito equations with a random or a W-symmetry
• Integrable Ito equations with multiple noises
• Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations