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 puts in evidence 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.
A symmetry-adapted numerical scheme for SDEs / F.C. De Vecchi, A. Romano, S. Ugolini. - In: JOURNAL OF GEOMETRIC MECHANICS. - ISSN 1941-4889. - 11:3(2019 Sep), pp. 325-359. [10.3934/jgm.2019018]
A symmetry-adapted numerical scheme for SDEs
F.C. De Vecchi;S. Ugolini
2019
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 puts in evidence 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.
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