A symmetry-adapted numerical scheme for SDEs

2017/04/30 by Francesco C. De Vecchi, Andrea Romanò, Andrea Romano +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Geometry #Homogeneous space #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Numerical analysis #Numerical methods for differential equations #Scheme (mathematics) #Symmetry (geometry) #cs.NA #math-ph #math.MP #math.NA #math.PR #msc:58D19 #msc:60H35

paper · pdf · doi:10.3934/jgm.2019018

published as Journal of Geometric Mechanics, 2019, 11 (3) : 325-359 · A numerical example added

openalex publication_date 2019/01/01 · arxiv created 2019/07/31 · arxiv updated 2020/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Numerical methods for nonlinear stochastic differential equations with jumps
• Continuous symmetries of difference equations
• Reduction and reconstruction of stochastic differential equations via symmetries
• Conservative methods for stochastic differential equations with a conserved quantity

Cited by

• Symmetries of stochastic differential equations using Girsanov transformations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps