Related papers: A Sharp First Order Analysis of Feynman-Kac Partic…
The Feynman-Kac equation governs the distribution of the statistical observable -- functional, having wide applications in almost all disciplines. After overcoming challenges from the time-space coupled nonlocal operator and the possible…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done…
In this paper, we are concerned with the numerical solution for the backward fractional Feynman-Kac equation with non-smooth initial data. Here we first provide the regularity estimate of the solution. And then we use the backward Euler and…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
We study the asymptotic convergence of the partial averaging method, a technique used in conjunction with the random series implementation of the Feynman-Kac formula. We prove asymptotic bounds valid for most series representations in the…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
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…
An efficient discrete time and space Markov chain approximation employing a Brownian bridge correction for computing curvilinear boundary crossing probabilities for general diffusion processes was recently proposed in Liang and Borovkov…
The single-mode approximation of the resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we…
For slowly evolving, discrete-time-dependent systems of difference equations (iterated maps), we believe the simplest means of demonstrating the validity of the averaging method at first order is by way of a lemma that we call Besjes'…
Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to…
In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…
We provide a mathematically rigorous derivation of the first order expansion of the motion of a charged particle in a strong magnetic field. In contrast to the derivations that can be found in the physics literature we solely assume…
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…
The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian Discrepancy Measure for testing precise statistical hypotheses. In particular, we derive results on third-order…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…