Related papers: Approximation order and approximate sum rules in s…

Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/…

We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order $N$ may be obtained in terms of a diagrammatic…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…

The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible stationary distributions. In the case of an…

A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…

We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…

In this paper, exact rate of decrease of best approximations of non-integer numbers by polynomials with integer coefficients of the growing exponentials is found on a disk in complex plane, on a cube in $\mathbb{R}^d$, and on a ball in…

Using the Green's function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some…

A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii)…

This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

We consider the problem of decomposing a regular non-negative function as a sum of squares of functions which preserve some form of regularity. In the same way as decomposing non-negative polynomials as sum of squares of polynomials allows…

An algorithm is presented to compute isolated values of the divisor summatory function in O(n^(1/3)) time and O (log n) space. The algorithm is elementary and uses a geometric approach of successive approximation combined with coordinate…

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…

We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…

We consider two seemingly unrelated questions: the relationship between nonnegative polynomials and sums of squares on real varieties, and sparse semidefinite programming. This connection is natural when a real variety $X$ is defined by a…

We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…