Multiple stochastic integrals with dependent integrators

Limit theorems for multiple stochastic integrals

We show that the general stable convergence results proved in Peccati and Taqqu (2007) for generalized adapted stochastic integrals can be used to obtain limit theorems for multiple stochastic integrals with respect to independently scattered random measures. Several applications are developed in a companion paper (see Peccati and Taqqu, 2008a), where we prove central limit results involving si...

Stochastic Lie Group Integrators

We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie alge...

Multiple integrals: Lagrangian Dependent on several minimizers

Inequalities for Stieltjes integrals with convex integrators and applications

Inequalities for a Grüss type functional in terms of Stieltjes integrals with convex integrators are given. Applications to the Čebyšev functional are also provided.

Stochastic variational integrators

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 result is to derive governing SDEs for such systems from a critical point of a stochastic action. Using this result, the paper derives Langevin-type equations for constrained mechanical systems and im...