A symmetry-adapted numerical scheme for SDEs

Abstract

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the symmetry properties of the equation is introduced. Our algorithmic procedure is applied to the family of general linear SDEs for which two theoretical estimates of the numerical forward error are established.

arXiv commentA numerical example added

References in corpus (7)

• Stochastic Variational Integrators
• Continuous Symmetries of Difference Equations
• Long-Run Accuracy of Variational Integrators in the Stochastic Context
• Variational Principles for Stochastic Soliton Dynamics
• Symmetries of Stochastic Differential Equations: a geometric approach
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Cited by in corpus (5)

• Symmetries of Stochastic Differential Equations using Girsanov transformations
• 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
• Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps