Related papers: A Value Region Problem for Continued Fractions and…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
The Euler scheme is one of the standard schemes to obtain numerical approximations of stochastic differential equations (SDEs). Its convergence properties are well-known in the case of globally Lipschitz continuous coefficients. However, in…
In this work, we present continued fractions for the arithmetic, geometric, harmonic and cotangent means of $[a_0,a_1,\dots,a_k]$ and $[a_0,a_1,\dots,a_k,a_{k+1}]$, and some of their applications.
Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential…
A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…
We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
We show that Stieltjes moment sequences are infinitely log-convex, which parallels a famous result that (finite) P\'olya frequency sequences are infinitely log-concave. We introduce the concept of $q$-Stieltjes moment sequences of…
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, including specific examples over reals, complex numbers,…
We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular…
We are concerned in this paper with the degenerate fractional diffusion advection equations posed in bounded domains. Due to a suitable formulation, we show the existence of weak entropy solutions for measurable and bounded initial and…
We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.
The problem of finding a martingale on a manifold with a fixed random terminal value can be solved by considering BSDEs with a generator with quadratic growth. We study here a generalization of these equations and we give uniqueness and…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…
Full indefinite Stieltjes moment problem is studied via the step-by-step Schur algorithm. Naturally associated with indefinite Stieltjes moment problem are generalized Stieltjes continued fraction and a system of difference equations,…
Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and distributed SDDs. The singular Lebesgue-Stieltjes measure is…
In this paper, one dimentional conformable fractional Dirac-type integro differential system is considered. The asymptotic formulae for the solutions, eigenvalues and nodal points are obtained. We investigate the inverse nodal problem and…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
We show several properties related to the structure of the family of classes of two-dimensional periodic continued fractions. This approach to the study of the family of classes of nonequivalent two dimexsional periodic continued fractions…
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…