Related papers: A laplace duality for integration

Let $\mathbb K(\mathbb R^d)$ denote the cone of discrete Radon measures on $\mathbb R^d$. The gamma measure $\mathcal G$ is the probability measure on $\mathbb K(\mathbb R^d)$ which is a measure-valued L\'evy process with intensity measure…

We consider the problem of finding a function defined on $(0,\infty)$ from a countable set of values of its Laplace transform. The problem is severely ill-posed. We shall use the expansion of the function in a series of Laguerre polynomials…

Integral representations for a complete set of linearly independent products of two solutions of the Airy equation whose arguments differ by $z_0$ are obtained using the Laplace contour integral method. This generalizes similar integral…

The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…

We investigate the approximation of generalized Laguerre- or Laplace-weighted integrals over $\mathbb{R}^d_+$ or $\mathbb{R}^d$ of functions from generalized Laguerre- or Laplace-weighted Sobolev spaces of mixed smoothness, respectively. We…

We consider the performance of non-optimal hedging strategies in exponential L\'evy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform…

We consider an optimal transport problem with backward martingale constraint. The objective function is given by the scalar product of a pseudo-Euclidean space $S$. We show that the supremums over maps and plans coincide, provided that the…

Let $K$ be a number field, let $A$ be a finite-dimensional $K$-algebra, let $\mathrm{J}(A)$ denote the Jacobson radical of $A$, and let $\Lambda$ be an $\mathcal{O}_{K}$-order in $A$. Suppose that each simple component of the semisimple…

This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…

For each $\lambda \in \mathbb N^*$, we consider the integral equation: \[ \int_{\lambda y} ^{\lambda x} f(t)\, d t = f(x) - f(y) \mbox{ for every $(x,y)\in {\mathbb R}_+^2$,} \] where $f$ is the concatenation of two continuous functions…

We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…

In this paper, we begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. By utilizing the solution to the Pythagorean equation $a^2 + b^2 = c^2$, these…

We are interested in the classical ill-posed Cauchy problem for the Laplace equation. One method to approximate the solution associated with compatible data consists in considering a family of regularized well-posed problems depending on a…

This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…

We present a systematic method for determining the two-loop effective Lagrangian resulting from integrating out a set of heavy particles in an ultraviolet scalar theory. We prove that the matching coefficients are entirely determined from…

From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…

In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S.…

In this note we prove the following good-$\lambda$ inequality, for $r>2$, all $\lambda > 0$, $\delta \in \big(0, \frac{1}{2} \big)$ \[ \nu\big\{ V_r(f) > 3 \lambda ; \mathcal{M}(f) \leq \delta \lambda\big\} \leq 4 \nu\{s(f) > \delta…

This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…