Related papers: Cylindrical continuous martingales and stochastic …

In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that…

Dzhaparidze and Spreij [5] showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This…

We introduce and discuss L\'evy-type cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a one-to-one relation to weak solutions of stochastic…

We study a stochastic optimal control problem for forward-backward control systems with quadratic generators. In order to establish the first and second-order variational and adjoint equations, we obtain a new estimate for one-dimensional…

We construct a pathwise calculus for functionals of integer-valued measures and use it to derive an martingale representation formula with respect to a large class of integer-valued random measures. Using these results, we extend the…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…

This paper is a follow-up on the \emph{noncommutative differential geometry on infinitesimal spaces} [15]. In the present work, we extend the algebraic convergence from [15] to the geometric setting. On the one hand, we reformulate the…

Sets of orthogonal martingales are importants because they can be used as stochastic integrators in a kind of chaotic representation property, see [20]. In this paper, we revisited the problem studied by W. Schoutens in [21], investigating…

This paper extends split variational inclusion problems to dynamic, stochastic, and multi-agent systems in Banach spaces. We propose novel iterative algorithms to handle stochastic noise, time-varying operators, and coupled variational…

We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…

We demonstrate that backward stochastic differential equations (BSDE) may be reformulated as ordinary functional differential equations on certain path spaces. In this framework, neither It\^{o}'s integrals nor martingale representation…

Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…

We combine two important recent advancements of MCMC algorithms: first, methods utilizing the intrinsic manifold structure of the parameter space; then, algorithms effective for targets in infinite-dimensions with the critical property that…

This paper contributes to the study of relative martingales. Specifically, for a closed random set $H$, they are processes null on $H$ which decompose as $M=m+v$, where $m$ is a c\`adl\`ag uniformly integrable martingale and, $v$ is a…

This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal…

This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between…

We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new exponential process is often merely a…

Our goal of this note is to give an easy proof that spaces of predictable processes with values in a Banach space are isomorphic to spaces of progressive resp. adapted, measurable processes. This provides a straightforward extension of the…