Related papers: Feynman-Kac Operator Expectation Estimator
We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…
The diffusion forecasting is a nonparametric approach that provably solves the Fokker-Planck PDE corresponding to It\^o diffusion without knowing the underlying equation. The key idea of this method is to approximate the solution of the…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
This paper proposes low-overhead and low-complexity channel estimation (CE) of frequency-domain equalization aided faster-than-Nyquist (FTN) signaling. In the proposed CE scheme, the concept of pilot superimposition is employed, where the…
Fourier Neural Operators (FNO) have emerged as promising solutions for efficiently solving partial differential equations (PDEs) by learning infinite-dimensional function mappings through frequency domain transformations. However, the…
In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale…
With the emergence of fluid antenna (FA) in wireless communications, the capability to dynamically adjust port positions offers substantial benefits in spatial diversity and spectrum efficiency, which are particularly valuable for mobile…
We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to…
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form elliptic equations. Based on the Feynman--Kac formula, the solution is represented as a conditional expectation associated with a diffusion…
Piecewise deterministic Markov process samplers are attractive alternatives to Metropolis--Hastings algorithms. A central design question is how to incorporate partial velocity refreshment to ensure ergodicity without injecting excessive…
We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage…
Distributed Mean Estimation (DME), in which $n$ clients communicate vectors to a parameter server that estimates their average, is a fundamental building block in communication-efficient federated learning. In this paper, we improve on…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
We provide two applications of an elementary (yet seemingly unknown) probabilistic representation of matrix ordered exponentials, which generalizes the Feynman-Kac formula in finite dimensions and the change of measure formula between two…
Functionals of a stochastic process Y(t) model many physical time-extensive observables, e.g. particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are…
Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the…
Diffusion coefficients are key thermophysical properties for modeling mass transport in liquids, but experimental data are scarce, making reliable prediction methods indispensable. In the present work, we introduce a new method for…
In this article, we prove a Feynman-Kac type result for a broad class of second order ordinary differential equations. The classical Feynman-Kac theorem says that the solution to a broad class of second order parabolic equations is the mean…
We provide a mathematical study of the modified Diffusion Monte Carlo (DMC) algorithm introduced in the companion article \cite{DMC}. DMC is a simulation technique that uses branching particle systems to represent expectations associated…