Stochastic discrete Hamiltonian variational integrators

• Published in: BIT Vol. 58; no. 4; pp. 1009 - 1048
• Main Authors: Holm, Darryl D., Tyranowski, Tomasz M.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2018; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computer simulation; Hamiltonian functions; Integrators; Lie groups; Mathematics; Mathematics and Statistics; Numeric Computing; Numerical stability; Runge-Kutta method; Stochastic differential equations; 65C30; Variational integrators; Geometric mechanics; Geometric numerical integration methods; Stochastic Hamiltonian systems
• ISSN: 0006-3835; 1572-9125; 1572-9125
• DOI: 10.1007/s10543-018-0720-2

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating functi...