Related papers: Pad\'e approximation for a multivariate Markov tra…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…
In this paper we consider the parameter estimation problem associated to partially-observed time changed SDEs, with observations that are given at discrete times. In particular we consider both likelihood and Bayesian estimation. We develop…
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
We present an approximation scheme for calculating observables and strength functions of finite fermionic systems at finite temperature such as hot nuclei. The approach is formulated within the framework of the Hubbard-Stratonovich…
Markov processes on the lattices with arbitrary dimension are omnipresent in statistical mechanics; however their algebraic description is complete only in dimension 1, for which linear algebra provides many tools complementary to the…
We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…
Approximation properties of multivariate Kantorovich-Kotelnikov type operators generated by different band-limited functions are studied. In particular, a wide class of functions with discontinuous Fourier transform is considered. The…
This paper is devoted to study the approximation properties and rate of approximation of the Szasz-Mirakjan-Kantrovich-Stancu type polynomials generated by the Dunkl generalization of the exponential function with respect to q -calculus. We…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
We introduce a new approach for deterministic sensitivity analysis of Markov reward processes, commonly used in cost-effectiveness analyses, via reformulation into a polynomial system. Our approach leverages cylindrical algebraic…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
To solve discrete Markov decision models with a large number of dimensions is always difficult (and at times, impossible), because size of state space and computation cost increases exponentially with the number of dimensions. This…
Evaluating the action of a matrix function on a vector, that is $x=f(\mathcal M)v$, is an ubiquitous task in applications. When $\mathcal M$ is large, one usually relies on Krylov projection methods. In this paper, we provide effective…
Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a non-compact space. Our motivation is to apply this result to measure-valued P\'olya processes (MVPPs, also…