arXiv research

New learning rates derived for Tikhonov-regularized problems without kernel assumptions.

Equivalence proven for isocapacitary mass notions.

Study Cheeger inequalities for Riemannian manifolds with boundary.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

Method approximates Lipschitz domains with smoother shapes.

The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.

The paper defines new constants for $p$-Laplacian on manifolds.

New mass definition linked to ADM mass for general metrics.

Proves conditions for Fourier transforms in rank 1 symmetric spaces.

In this article, we propose the notion of the general $p$-affine capacity and prove some basic properties for the general $p$-affine capacity, such as affine invariance and monotonicity. The newly proposed general $p$-affine capacity is compared with several classical geometric quantities, e.g., the volume, the $p$-var…

The paper uses Fourier integral theorem for estimating multivariate distributions.

Random Fourier features improve tabular deep learning convergence.

FNN approximates functions and solves PDEs with periodic BCs.

Random Fourier features classification achieves fast learning rates with fewer features.

New algorithms learn sparse set functions in non-orthogonal Fourier bases.

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff funct…

Fourier methods fail to accurately approximate option Greeks in realistic market conditions.

The paper derives statistics of multi-factor functions from their Fourier transforms.

New method for optimizing risk in financial models using Fourier transforms.

The paper studies Fourier-Laplace transforms in polynomial OU volatility models for option pricing.

A new model captures complex event data using attention and Fourier kernels.

Three RFF-based methods for nonlinear causal discovery in mixed data.

We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and computed using the fast F…

We systematically develop a transform of the Fourier-Mukai type for sheaves on symplectic manifolds $X$ of any dimension fibred in Lagrangian tori. One obtains a bijective correspondence between unitary local systems supported on Lagrangian submanifolds of $X$ and holomorphic vector bundles with compatible unitary conn…

This work improves Fourier pricing for multi-asset options using RQMC with domain transformation.

EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.

The paper bounds Fourier integral operators on Hardy spaces with specific conditions.

The classical shift retrieval problem considers two signals in vector form that are related by a shift. The problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shi…

In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an ele…

Extend classical theory of affine processes to path-dependent setting

FNSDA adapts to new dynamics via Fourier space adaptation.

Study Fourier estimator for spot volatility with unbounded coefficients and jumps.

We introduce the formalism of generalized Fourier transforms in the context of risk management. We develop a general framework to efficiently compute the most popular risk measures, Value-at-Risk and Expected Shortfall (also known as Conditional Value-at-Risk). The only ingredient required by our approach is the knowle…

New method detects bearing faults using multivariate statistical process control.

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs), introduced in [21], uses a uniform space grid. In this paper we utilize a tree-like spatial discretization that approximates the BSDE on the tree, so that no spatial interpolation procedure is necessary. In…

Proposes using GANs to solve phase retrieval problems.

A neural network method estimates densities from characteristic functions.

Quantum-assisted Gaussian process speeds up data regression.

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main appli…

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic…

Paper proves Fourier transform for valuations, simplifying previous work.

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is cons…

A new algorithm computes Fourier coefficients for a specified range efficiently.

Establish a unified framework for negative results in Fourier analysis.

NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.

Improved electrical load forecasting model using Fourier-enhanced RNN.

Study approximates operator learning for PDEs using Fourier multipliers.

RNNs solve modular addition tasks using low rank and sparse Fourier structures.