Related papers: A note on a variance bound for the multinomial and…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…

We give (1) an upper bound on the denominators of numerical boundary slopes and (2) an upper bound on the differences between two numerical boundary slopes, for Montesinos knot exteriors.

In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type $$\cases{-\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k)\hskip 10pt k=1,...,n, \cr & \cr x_0=x_{n+1}=0\cr}$$…

Chernoff approximations to strongly continuous one-parameter semigroups give solutions to a wide class of differential equations. This paper studies the rate of convergence of the Chernoff approximations. We provide simple natural examples…

We show a lower estimate of the Milnor number of an isolated hypersurface singularity, via its Newton number. We also obtain analogous estimate of the Milnor number of an isolated singularity of a similar complete intersection variety.

In this note we consider roots of multivariate polynomials over a finite grid. When given information on the leading monomial with respect to a fixed monomial ordering, the footprint bound [8, 5] provides us with an upper bound on the…

We give lower bounds on the case of worst inhomogeneous approximation.

We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for…

In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…

We improve constants in the Rademacher-Menchov inequality.

This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…

In this paper, we prove a local limit theorem and a refined continuity correction for the negative binomial distribution. We present two applications of the results. First, we find the asymptotics of the median for a…

We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…

We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…

We prove existence of positive solutions to a nonlinear fractional boundary value problem. Then, under some mild assumptions on the nonlinear term, we obtain a smart generalization of Lyapunov's inequality. The new results are illustrated…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.