Related papers: Discrete approximation of functionals with jumps a…

We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

We study a discrete approximation of functionals depending on nonlocal gradients. The discretized functionals are proved to be coercive in classical Sobolev spaces

The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…

We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.

We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…

We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof…

We consider equidistant approximations of stochastic integrals driven by H\"older continuous Gaussian processes of order $H>\frac12$ with discontinuous integrands involving bounded variation functions. We give exact rate of convergence in…

We approximate functionals depending on the gradient of $u$ and on the behaviour of $u$ near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise…

In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…

We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…

We survey the classical results of the Dirichlet Approximation Theorem.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…

In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…

In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier…

We study properties of functions with bounded variation in Carnot-Ca\-ra\-th\'eo\-do\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of…

The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional It\^o diffusion that almost surely converges to a weak solution of the given stochastic differential equation. Under suitable conditions, the…

This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary $L_p$-norms ($1 \leq p \leq \infty)$. We prove the existence of best approximations und derive…