Reduction and reconstruction of stochastic differential equations via symmetries

Abstract

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance.

References in corpus (5)

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• Variational Principles for Stochastic Fluid Dynamics
• An averaging principle for a completely integrable stochastic Hamiltonian system
• Noise and dissipation on coadjoint orbits
• Symmetries of Stochastic Differential Equations: a geometric approach

Cited by in corpus (9)

• Symmetries of Stochastic Differential Equations using Girsanov transformations
• A note on symmetries of diffusions within a martingale problem approach
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
• A symmetry-adapted numerical scheme for SDEs
• Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps
• Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
• On the integration of Ito equations with a random or a W-symmetry
• Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations