Related papers: Corrections and acknowledgment for ``Local limit t…
We correct a few errors that appeared in [Convergence of invariant measures for singular stochastic diffusion equations, Stochastic Process. Appl. 122 (2012), no. 4, 1998--2017] by I. Ciotir and J.M. T\"olle.
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…
We consider the problem of detecting abrupt changes (i.e., large jump discontinuities) in the rate function of a point process. The rate function is assumed to be fully unknown, non-stationary, and may itself be a random process that…
Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
We investigate higher derivative corrections in M-theory by applying Noether's method. Cancellation of variations, which contain linear terms in 4-form field strength, under local supersymmetry is executed with the aid of computer…
We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
We prove the Local Limit Theorems for bounded additive functionals of uniformly elliptic inhomogeneous Markov arrays. As an application we obtain the precise asymptotics in the large deviation regime for bounded additive functionals of…
I discuss the calculation of the next-to-leading logarithmic (NLL) corrections to the BFKL resummation, as well as some of the issues that arise in this formalism at NLL. In particular I consider the large size and apparent instability of…
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
We correct the second main theorem of the previous paper "A perturbation of the Dunkl harmonic oscillator on the line", by the first two authors. The corrections concern mainly certain estimates, which were also improved by adding more…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
Unfortunately, the article "A Comparative Study to Benchmark Cross-project Defect Prediction Approaches" has a problem in the statistical analysis which was pointed out almost immediately after the pre-print of the article appeared online.…