Pathwise Accuracy and Ergodicity of Metropolized Integrators for SDEs (2009)
Bou-Rabee, Nawaf, Vanden-Eijnden, Eric
Metropolized integrators for ergodic stochastic differential equations (SDE) are proposed which (i) are ergodic with respect to the (known) equilibrium distribution of the SDE and (ii) approximate...
Stochastic variational integrators (2009)
Bou-Rabee, Nawaf, Owhadi, Houman
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein–Uhlenbeck theory of Brownian motion in a force field. The main...
Bou-Rabee, Nawaf, Marsden, Jerrold E.
In this paper, structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton–Pontryagin variational principle. From this principle, one can...
Stochastic variational integrators (2009)
Bou-Rabee, Nawaf, Owhadi, Houman
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein–Uhlenbeck theory of Brownian motion in a force field. The main...
Bou-Rabee, Nawaf, Marsden, Jerrold E.
In this paper structure-preserving time-integrators for rigid body-type mechanical systems are derived from a discrete Hamilton-Pontryagin variational principle. From this principle one can derive a...
Boltzmann-Gibbs Preserving Langevin Integrators (2007)
Bou-Rabee, Nawaf, Owhadi, Houman
This paper analyses a class of structure-preserving Langevin integrators obtained from a Lie-Trotter splitting of the Langevin equations into Hamilton's and Ornstein-Uhlenbeck equations. The schemes...
Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums (2007)
Bou-Rabee, Nawaf, Owhadi, Houman
This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with non-degenerate...
Ballistic Transport at Uniform Temperature (2007)
Bou-Rabee, Nawaf, Owhadi, Houman
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body...
Stochastic Variational Partitioned Runge-Kutta Integrators for Constrained Systems (2007)
Bou-Rabee, Nawaf, Owhadi, Houman
Stochastic variational integrators for constrained, stochastic mechanical systems are developed in this paper. The main results of the paper are twofold: an equivalence is established between a...
Stochastic Variational Integrators (2007)
Bou-Rabee, Nawaf, Owhadi, Houman
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds. The main result is to derive stochastic governing equations for such systems from a...
Hamilton-Pontryagin integrators on Lie groups (2007)
In this thesis structure-preserving time integrators for mechanical systems whose configuration space is a Lie group are derived from a Hamilton-Pontryagin (HP) variational principle. In addition to...
Hamilton-Pontryagin integrators on Lie groups (2007)
In this thesis structure-preserving time integrators for mechanical systems whose configuration space is a Lie group are derived from a Hamilton-Pontryagin (HP) variational principle. In addition to...
In the name of Allah, the Most Beneficient, the Most Merciful Sura 93 Ad-Dhuha (full morning light) Translation by Ustadh Abdullah Yusuf Ali By the full morning light, And by the night when it is...