Related papers: Clark--Ocone formula and variational representatio…

We investigate a novel connection between the weighted isoperimetric problems and the weighted Poisson integrals of the extension problems for nonlocal elliptic operators. We first derive sharp inequalities for the weighted Poisson…

Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…

The Mittag-Leffler function $E_{\alpha}$ being a natural generalization of the exponential function, an infinite-dimensional version of the fractional Poisson measure would have a characteristic functional \[ C_{\alpha}(\phi)…

We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite…

Previously developed method for finding asymptotic solutions of Vlasov equations using two-dimensional (in coordinate x and time t) Laplace transform is applied to low-collision electron-ion plasmas. Taking into account Coulomb collisions…

In this paper we explore the fundamentals of the Martingale Representation Theorem (MRT) and a closely related result, the Clark-Ocone formula. We also investigate how far these theorems can be taken, notably beyond the regular Sobolev…

We consider nonlinear filters for diffusion processes when the observation and signal noises are small and of the same order. As the noise intensities approach zero, the nonlinear filter can be approximated by a certain variational problem…

We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon$, the solution exhibits…

The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It can not be used as a local minimization principle while…

This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…

This paper examines solutions to the Laplace equation using analytical techniques, including separation of variables and the Poisson integral formula, and probabilistic methods, such as Brownian motion. We address applications to imaging,…

In this paper, a large deviation principle for the strong solution of the p-Laplace equation on unbounded domain driven by small multiplicative Brownian noise is established. The weak convergence approach and the localized time increment…

Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the difference operator of Malliavin calculus. Poisson functionals,…

We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals…

This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…

In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…

We develop walk-on-sphere for fractional Poisson equations with Dirichilet boundary conditions in high dimensions. The walk-on-sphere method is based on probabilistic represen tation of the fractional Poisson equation. We propose effcient…

We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…

We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the…

We present versions of several classical results on harmonic functions and Poisson boundaries in the setting of locally compact quantum groups. In particular, the Choquet--Deny theorem holds for compact quantum groups; also, the result of…