Geometric Euler--Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n)

DOI10.1137/15M1019726zbMath1347.65015OpenAlexW2515882314WikidataQ115246971 ScholiaQ115246971MaRDI QIDQ2817779

Victor Solo, Marc James Piggott

Publication date: 2 September 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1019726

zbMATH Keywords

algorithmconvergencestrong convergencenumerical examplesPadé approximationgeometric integrationCayley transformquadratic Lie groupEuler-Maruyamaexponential Rodrigues formulastochastic Lie group integrators

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (4)

Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies ⋮ Strong stochastic Runge-Kutta-Munthe-Kaas methods for nonlinear Itô SDEs on manifolds ⋮ Leader-Following Rendezvous Control for Generalized Cucker-Smale Model on Riemannian Manifolds ⋮ Higher strong order methods for linear Itô SDEs on matrix Lie groups

Uses Software

• MATLAB expm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A class of orthogonal integrators for stochastic differential equations
• Stochastic models, information theory, and Lie groups. II: Analytic methods and modern applications
• Exponentials of skew-symmetric matrices and logarithms of orthogonal matrices
• Generalized polar coordinates on Lie groups and numerical integrators
• The Landau equation for Maxwellian molecules and the Brownian motion on \(\mathrm{SO}_N(\mathbb R)\)
• High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula
• Lower bounds for the condition number of Vandermonde matrices
• One step semi-explicit methods based on the Cayley transform for solving isospectral flows
• High order Runge-Kutta methods on manifolds
• Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups
• Runge-Kutta methods on Lie groups
• On the construction of geometric integrators in the RKMK class
• Lie-Butcher theory for Runge-Kutta methods
• The ordinary differential equation approach to asymptotically efficient schemes for solution of stochastic differential equations
• Numerical approximation of diffusions in \(\mathbb {R}^d\) using normal charts of a Riemannian manifold
• Order Conditions of Stochastic Runge--Kutta Methods by B-Series
• A Lie Algebraic Approach to Numerical Integration of Stochastic Differential Equations
• Interest rate models on Lie groups
• Numerical methods for strong solutions of stochastic differential equations: an overview
• Brownian Processes for Monte Carlo Integration on Compact Lie Groups
• Brownian motions on the $3$-dimensional rotation group
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Stochastic Lie Group Integrators
• Stochastic variational integrators
• Efficient Strong Integrators for Linear Stochastic Systems
• Brownian Motion on a submanifold of Euclidean Space
• [https://portal.mardi4nfdi.de/wiki/Publication:4121258 Stabilit� des solutions des �quations diff�rentielles stochastiques application aux int�grales multiplicatives stochastiques]
• The Sensitivity of the Matrix Exponential
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
• Approximating the exponential from a Lie algebra to a Lie group
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Motion estimation via dynamic vision
• Stochastic expansions and Hopf algebras
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Runge–Kutta Methods for the Strong Approximation of Solutions of Stochastic Differential Equations
• Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions
• Brownian motions in a Lie group
• Integration methods based on canonical coordinates of the second kind
• On Cayley-transform methods for the discretization of Lie-group equations

This page was built for publication: Geometric Euler--Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n)