Fetching the paper…
Reading the bibliography…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics.
Mecanique aleatoire
J. Bismut · 1982
Earlier work this paper cites.
Theory of RF acceleration
G. Dôme · 1987
Earlier work this paper cites.
Stochastic mechanics and random fields
E. Nelson · 1988
Earlier work this paper cites.
Stochastic Differential Equations and Diffusion Processes
N. Ikeda and S. Watanabe · 1989
Earlier work this paper cites.
Symplectic integrators for Hamiltonian problems: an overview
J. M. Sanz-Serna · 1992
Earlier work this paper cites.
Solving Ordinary Differential Equations I: Nonstiff Problems
E. Hairer, S. Nørsett, and G. Wanner · 1993
Earlier work this paper cites.
Introduction to Mechanics and Symmetry
J. Marsden and T. Ratiu · 1994
Earlier work this paper cites.
Simulation of one-dimensional noisy Hamiltonian systems and their application to particle storage rings
M. Seeßelberg, H. P. Breuer, H. Mais, F. Petruccione, and J. Honerkamp · 1994
Earlier work this paper cites.
The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions
C. Soize · 1994
Earlier work this paper cites.
Numerical Solution of Stochastic Differential Equations
P. Kloeden and E. Platen · 1995
Earlier work this paper cites.
Numerical Integration of Stochastic Differential Equations
G. Milstein · 1995
Earlier work this paper cites.
High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations
K. Burrage and P. M. Burrage · 1996
Earlier work this paper cites.
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
E. Hairer and G. Wanner · 1996
Earlier work this paper cites.
Stochastic Flows and Stochastic Differential Equations
H. Kunita · 1997
Earlier work this paper cites.
General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems
K. Burrage and P. M. Burrage · 1998
Earlier work this paper cites.
Multisymplectic geometry, variational integrators, and nonlinear PDEs
J. E. Marsden, G. W. Patrick, and S. Shkoller · 1998
Earlier work this paper cites.
Ergodicity of dissipative differential equations subject to random impulses
J. Sanz-Serna and A. Stuart · 1999
Earlier work this paper cites.
Order Conditions of Stochastic Runge–Kutta Methods by B-Series
K. Burrage and P. M. Burrage · 2000
Earlier work this paper cites.
Discrete mechanics and variational integrators
J. E. Marsden and M. West · 2001
Earlier work this paper cites.
Symplectic integration of Hamiltonian systems with additive noise
G. N. Milstein, Y. M. Repin, and M. V. Tretyakov · 2001
Earlier work this paper cites.
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
E. Hairer, C. Lubich, and G. Wanner · 2002
Earlier work this paper cites.
Numerical methods for stochastic systems preserving symplectic structures
G. N. Milstein, Y. M. Repin, and M. V. Tretyakov · 2002
Earlier work this paper cites.
Variational integrators for degenerate Lagrangians, with application to point vortices
C. W. Rowley and J. E. Marsden · 2002
Earlier work this paper cites.
Stochastic Hamiltonian systems: Exponential convergence to the invariant measure, and discretization by the implicit Euler scheme
D. Talay · 2002
Cited alongside, same era.
Asynchronous variational integrators
A. Lew, J. E. Marsden, M. Ortiz, and M. West · 2003
Cited alongside, same era.
Splitting for dissipative particle dynamics
T. Shardlow · 2003
Cited alongside, same era.
Implicit stochastic Runge–Kutta methods for stochastic differential equations
K. Burrage and T. Tian · 2004
Cited alongside, same era.
Runge–Kutta methods for Stratonovich stochastic differential equation systems with commutative noise
A. Rößler · 2004
Cited alongside, same era.
Stochastic Integration and Differential Equations
P. Protter · 2005
Cited alongside, same era.
Symplectic numerical schemes for stochastic systems preserving Hamiltonian functions
C. Anton, Y. S. Wong, and J. Deng · 2013
Later among the works it cites.
Stochastic Differential Equations: Theory and Applications
L. Arnold · 2013
Later among the works it cites.
R-adaptive multisymplectic and variational integrators
T. M. Tyranowski and M. Desbrun · 2013
Later among the works it cites.
Variational partitioned Runge-Kutta methods for Lagrangians linear in velocities
T. M. Tyranowski and M. Desbrun · 2013
Later among the works it cites.
Weak symplectic schemes for stochastic Hamiltonian equations
C. Anton, J. Deng, and Y. S. Wong · 2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Geometric integrators for ODEs
R. I. McLachlan and G. R. W. Quispel · 2006
Cited alongside, same era.
Stochastic variational partitioned Runge-Kutta integrators for constrained systems
N. Bou-Rabee and H. Owhadi · 2007
Cited alongside, same era.
Stochastic Differential Equations and Applications
X. Mao · 2007
Cited alongside, same era.
Second order Runge–Kutta methods for Stratonovich stochastic differential equations
A. Rößler · 2007
Cited alongside, same era.
Variational Integrators and Generating Functions for Stochastic Hamiltonian Systems
L. Wang · 2007
Cited alongside, same era.
Stochastic Hamiltonian Dynamical Systems
J. A. Lázaro-Camí and J. P. Ortega · 2008
Cited alongside, same era.
Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise
P. M. Burrage and K. Burrage · 2014
Later among the works it cites.
High-order symplectic schemes for stochastic Hamiltonian systems
J. Deng, C. Anton, and Y. S. Wong · 2014
Later among the works it cites.
A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects
J. Vankerschaver and M. Leok · 2014
Later among the works it cites.
Generating functions for stochastic symplectic methods
L. Wang and J. Hong · 2014
Later among the works it cites.
Spectral variational integrators
J. Hall and M. Leok · 2015
Later among the works it cites.
Preservation of quadratic invariants of stochastic differential equations via Runge–Kutta methods
J. Hong, D. Xu, and P. Wang · 2015
Later among the works it cites.
Stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with multiplicative noise
Q. Ma and X. Ding · 2015
Later among the works it cites.
Construction and analysis of higher order Galerkin variational integrators
S. Ober-Blöbaum and N. Saake · 2015
Later among the works it cites.
Variational principles for stochastic soliton dynamics
D. D. Holm and T. M. Tyranowski · 2016
Closest in time.
Partial differential equations and stochastic methods in molecular dynamics
T. Lelièvre and G. Stoltz · 2016
Closest in time.
Stochastic symplectic methods based on the Padé approximations for linear stochastic Hamiltonian systems
L. Sun and L. Wang · 2016
Closest in time.
Order conditions for stochastic Runge–Kutta methods preserving quadratic invariants of Stratonovich SDEs
S. Anmarkrud and A. Kværnø · 2017
Closest in time.
High order conformal symplectic and ergodic schemes for the stochastic Langevin equation via generating functions
J. Hong, L. Sun, and X. Wang · 2017
Closest in time.
Galerkin variational integrators and modified symplectic Runge–Kutta methods
S. Ober-Blöbaum · 2017
Closest in time.
Construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems
P. Wang, J. Hong, and D. Xu · 2017
Closest in time.
Stochastic symplectic Runge–Kutta methods for the strong approximation of Hamiltonian systems with additive noise
W. Zhou, J. Zhang, J. Hong, and S. Song · 2017
Closest in time.
New variational and multisymplectic formulations of the Euler–Poincaré equation on the Virasoro–Bott group using the inverse map
D. D. Holm and T. M. Tyranowski · 2018
Closest in time.