Related papers: A general framework for variational calculus on Wi…

We give a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}|\mathcal{F}_t\right]$ for a large class of measures $\nu$. We give a refined entropic characterization of the invertibility of some perturbations of the identity. We…

We expand the classic variational formulation of $-\log\mathbb{E}\left[e^{-f}\right]$ to the case where f depends on a diffusion, and not only a on Brownian motion, while decreasing the integrability hypothesis on f. We also give an…

In this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an…

Let $(W,H,\mu)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity where the perturbation $u$ is an equivalence class w.r.to the Wiener measure. We study several necessary and sufficient conditions…

The set of closed (or holonomic) measures provides a useful setting for studying optimization problems because it contains all curves, while also enjoying good compactness and convexity properties. We study the way to do variational…

In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…

Let h be a real-analytic function in the neighborhood of some compact set K on the plane. We show that for any complex measure on the Euclidean space of a finite total variation without singular components with the Fourier--Stieltjes…

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…

For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an $\hbox{Ad}$-invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem…

In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that…

In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schr\"odinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost…

Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure $\mu_0$ on self-avoiding loops in ${\mathbb C} \setminus\{0\}$ which surround $0$. Our first major objective is…

Using a local analog of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent…

We define a capacity C on abstract Wiener spaces and prove that, for any u with bounded variation, the total variation measure |Du| is absolutely continuous with respect to C: this enables us to extend the usual rules of calculus in many…

We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…

Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…

We consider an inverse extremal problem for variational functionals on arbitrary time scales. Using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variational functional that attains a…

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…