Related papers: Existence of limit of multivariable function
We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…
In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…
We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.
We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…
The central limit theorem, the invariance principle and the Poisson limit theorem for the hierarchy of freeness are studied. We show that for given natural m the limit laws can be expressed in terms of non-crossing partitions of depth…
A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.
The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type.
We prove a version of L'hospital's rule for multivariable functions, which holds for non-isolated singular points. We also give an algorithm for resolving many indeterminate limits with isolated singular points.
In this work we establish local limit theorems for q-multinomial and multiple Heine distributions. Specifically, the pointwise convergence of the q-multinomial distribution of the first kind, as well as for its discrete limit, the multiple…
An algorithm for computing the limit of a quotient of bivariate real analytic functions has been developed by one of the authors in (Limits of quotients of bivariate real analytic functions, Journal of Symbolic Computation, 50, 2013, 197…
There are given conditions for represention of a function of many arguments as the difference of convex functions.
This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local…
Let $f: \mathbb{N}^2 \mapsto \mathbb{C}$ be an arithmetic function of two variables. We study the existence of the limit: \[\displaystyle \lim_{x \to \infty} \frac{1}{x^2 (\log x)^{k-1}} \sum_{n_1 , n_2 \le x} f (n_1, n_2) \] where $k$ is a…
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.
For students and their lecturers and instructors interested in the natural problem of a possible generalization of l'Hopital's rule for functions depending on two or more variables, we offer our approach. For instructors, we discuss the…
We investigate the boundary behavior of holomorphic functions with respect to a family of curves in a domain of finite type. This work is a generalization of \u{C}irka's classical result on the unit ball and it supplements the result by…
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of…
The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…
This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.