Given a sequence of independent standard Gaussian variables (Zn), the classical Pisier algebra P is the class of all continuous functions f on the unit circle T such that for each t ∈ 𝕋, the random Fourier series \( {\sum}_{n\in \mathrm{\mathbb{Z}}}{Z}_n\hat{f}(n)\times \exp \left(2\pi \mathrm{i} nt\right) \) converges in L2 and the corresponding sums constitute a Gaussian process that admits a continuous

We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under minimal moment conditions.

We introduce a new option pricing equation with noise in a frictional financial market, which is fully different from the classical option pricing equation, and arrive at the existence of martingale solutions of this option pricing equation regardless of incompressibility. Furthermore, we also discuss the uniqueness of martingale solutions.

We study the distribution of the zeros of the kth derivatives of the functions belonging to the extended Selberg class. We obtain the zero-free regions for these derivatives and a Riemann–von Mangoldt-type estimate of the count of their nontrivial zeros.

Abstract. This research paper stands for the estimation of the precision matrix of the normal matrix with monotone missing data. We explicitly provide maximum and expectation a posteriori estimators. For this purpose, we basically use an extension of the Wishart distribution, that is, the Riesz distribution on symmetric matrices. We prove that some of the latter distributions may be presented using

Abstract. Let X = (X(t))t≥0 (X(0) = 0) be a continuous centered Gaussian process on a probability space (Ω,F,P), and let (Yt)t∈[0,1] (Y0 = 0) be a continuous process (on the same probability space) with nondecreasing paths, independent of X. Define the time-changed Gaussian process Zt = X(Yt), t ∈ [0, 1]. In this paper, we investigate a problem of finite-dimensional large deviations and a problem of

Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching process with regularly varying immigration having index α ∈ (0, 2). We show that limits of finite-dimensional distributions of appropriately centered and scaled aggregated partial-sum processes exist when first taking the limit as N → ∞and then

Abstract. We show that, under the long-tailedness of the densities of normalized Lévy measures, the densities of infinitely divisible distributions on the half-line are subexponential if and only if the densities of their normalized Lévy measures are subexponential. Moreover, we prove that, under a certain continuity assumption, the densities of infinitely divisible distributions on the half-line are

For sequences of d + 1 signs + and − beginning with a + and having exactly two variations of sign, we give some sufficient conditions for the (non)existence of degree d real univariate polynomials with such signs of the coefficients and having given numbers of positive and negative roots compatible with Descartes’ rule of signs.

In this paper, we present a switching property for squared Bessel process. We prove that the starting point and the time parameter can be in a sense switched. As a consequence, we obtain new distributional dependencies among a squared Bessel process R, a Brownian motion with drift \( {B}^{\left(\mu \right)},\mu \ge 0,\left({B}_t^{\left(\mu \right)}:= {B}_t+\mu t\kern0.5em \mathrm{for}\ \mathrm{a}\

We consider themain boundary value problems of linear elastostatics with nonregular data. We prove existence and uniqueness results for bounded and exterior domains of ℝ3 of class Ck (k ⩾ 2). In the case of isotropic body, we prove the results for domains of class C1,α (α ∈ (0, 1]) and of class C1 in the case of the displacement problem.

We evaluate a weighted sum of Gauss hypergeometric functions for certain ranges of the argument, weights and parameters. We establish the domain of absolute convergence of this series by determining the growth of the hypergeometric function for large summation index. We present an application to Galton–Watson branching processes arising in the theory of stochastic processes. We introduce a new class

In the metadata of the article on SpringerLink, the corresponding author is incorrect. The corresponding author is Tran Loc Hung (tlhung@ufm.edu.vn; tlhungvn@gmail.com)

In this paper, we prove an existence and uniqueness theorem and a comparison theorem for a class of anticipated mean-field backward stochastic differential equations with jumps.

Let f be the characteristic function of a probability measure μf on ℝn, and let σ > 0. We study the following extrapolation problem: under what conditions on the neighborhood of infinity Vσ = {x ∈ ℝn : |xk| > σ, k = 1, …n} in ℝndoes there exist a characteristic function g on ℝn, such that g = f on Vσ but g ≢ f? Let μf have a nonzero absolutely continuous part with continuous density 𝜑. In this paper

We present upper bounds of the integral \( {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathrm{P}\left\{{Z}_N0\left({S}_N{X}_1+\dots +{X}_N\right) \) of centered random variables X1,X2, . . . satisfying the uniformly strong mixing condition. The number of summands N is a nonnegative integer-valued random variable independent of X1,X2, . . . .

Let X and Y be two independent random variables with corresponding distributions F and G on [0,∞). The distribution of the product XY , which is called the product convolution of F and G, is denoted by H. In this paper, we give some suitable conditions on F and G, under which the distribution H belongs to the long-tailed distribution class. Here F is a generalized long-tailed distribution, not necessarily

We derive exponential bounds for the tail of the distribution of normalized sums of triangular arrays of random variables, not necessarily independent, under the law of ordinary logarithm. Furthermore, we provide estimates for partial sums of triangular arrays of independent random variables belonging to suitable grand Lebesgue spaces and having heavy-tailed distributions.

We consider nonparametric estimation of the ridge of a probability density function for multivariate linear processes with long-range dependence. We derive functional limit theorems for estimated eigenvectors and eigenvalues of the Hessian matrix. We use these results to obtain the weak convergence for the estimated ridge and asymptotic simultaneous confidence regions.

Investigating the same problems for linear random fields with tapered innovations, I realized that the Hurst index of the limit FBM process and conditions on tapering parameter γ in Theorem 1 were incorrectly calculated.

In this paper, we consider a strictly stationary sequence of m-dependent random variables through a compatible sequence of independent and identically distributed random variables by the moving averages processes. Using the Zolotarev distance, we estimate some rates of convergence in the weak limit theorems for normalized geometric random sums of the strictly stationary sequence of m-dependent random

We establish a central limit theorem for counting large continued fraction digits (an), that is, we count occurrences {an>bn}, where (bn) is a sequence of positive integers. Our result improves a similar result by Philipp, which additionally assumes that bn tends to infinity. Moreover, we give a refinement of the famous Borel–Bernstein theorem for continued fractions regarding the event that the nth

In this paper, we study the multiplicity of solutions for a class of nonhomogeneous Schrödinger–Poisson systems under general superlinear conditions at infinity. With the aid of Ekeland’s variational principle, Jeanjean’s monotone method, Pohožaev’s identity, and the mountain pass theorem, we prove that a Schrödinger–Poisson system has at least two positive solutions, which generalizes and improves

In this paper, we study some asymptotic properties of CFG estimator of the Pickands dependence function of strictly stationary absolutely regular sequences of bivariate extremes. We then propose an asymptotic test of independence of the vector margins. Finite sample properties of the estimate are investigated by simulation.

The aim of this paper is to present newupper bounds for the distance between a properly normalized permanent of a rectangular complex matrix and the product of the arithmetic means of the entries of its columns. It turns out that the bounds improve those from earlier work. Our proofs are based on some new identities for the above-mentioned difference and also for related expressions for matrices over

Consider a nonstandard renewal risk model in which claims and interarrival times form a sequence of independent and identically distributed random pairs, with each pair obeying arbitrary dependence or size-dependence structure. In the case of heavy-tailed claims, we obtain the asymptotic behavior of finite-time ruin probability with the uniformity in time in some infinite regions.

In this paper, we extend to CKLS and CEV processes a known result on weak approximation of CIR processes by discrete random variables. Namely, for CKLS and CEV processes, we construct first-order split-step weak approximations that use generation of two-valued random variables at each discretization step. The accuracy of constructed approximations is illustrated by several simulation examples.

In this paper, we consider the Dirichlet problem for a nonlinear wave equation with Balakrishnan–Taylor term. We establish the local existence is established by the linearization method together with the Faedo–Galerkin method. Next, we prove an exponential energy decay result by suitable Lyapunov functionals.

In this paper, we propose and analyze numerical treatment for a singularly perturbed convection–diffusion boundary value problem with nonlocal condition. First, the boundary layer behavior of the exact solution and its first derivative have been estimated. Then we construct a finite difference scheme on a uniform mesh. We prove the uniform convergence of the proposed difference scheme and give an error

Consider a continuous-time process {ZNt}, where {Zn} is a Galton–Watson process with offspring mean m, and {Nt} is a Poisson process independent of {Zn}. It turns out that Rt := ZNt+1/ZNt is an estimator of m. We deal with large deviation rates for the convergence of Rt to m for the supercritical and critical cases.

In this paper, we propose a new method of upper bounds for the number of integer polynomials of the fourth degree with a given discriminant. By direct calculation similar results were established by H. Davenport and D. Kaliada for polynomials of second and third degrees.

It is known that there exist only finitely many trivial solutions of a certain Diophantine equation over number fields except for the case the rational number field. In this paper, we calculate an explicit upper bound of the solution-free region.

We give new proofs of some known results on the values of the Riemann zeta function at positive integers and obtain some new theorems related to these values. Considering even zeta values as ζ(2n) = ηnπ2n, we obtain the generating functions of the sequences ηn and (−1)nηn. Using the Riemann–Lebesgue lemma, we give recurrence relations for ζ(2n) and ζ(2n + 1). Furthermore, we prove some series equations

We prove that, for given positive numbers α and h, the Riemann zeta-function ζ can approximate any nonvanishing analytic function on a simply connected compact subset of the right open half of the critical strip by shifts of type ζ(s + ih⌊αn⌋).

In this paper, we study the value distribution of L-functions in the Selberg class and concentrate on the uniqueness questions of L-functions that share one or two sets with an arbitrary meromorphic function. The results obtained in this paper improve the recent results due to Q.-Q. Yuan, X.-M. Li, and H.-X. Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J.

Let f(z) be a primitive holomorphic cusp form of even integral weight k for the full modular group. Denote its nth normalized Fourier coefficient (Hecke eigenvalue) by λf (n). Let a(n) be the function with squarefull kernel. In this paper, we establish that \( {\sum}_{n\leqslant x}a(n){\lambda}_f^2\left(n+1\right)= Cx+O\left({x}^{13/14+\upepsilon}\right) \), where C is a constant that can be explicitly

In the paper, we consider the partial-sum process \( {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, \) where \( \left\{{X}_n^{(n)},k\in \mathbb{Z}\right\},n\ge 1, \) is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter bn depending on n. We show that, depending on the properties of a filter of a linear process under consideration and on the