Related papers: Local theorems for arithmetic compound renewal pro…

We investigate performance of approximations put forth in \citeNP{[Malinovskii 2017a]} and \citeNP{[Malinovskii 2017b]} for the distribution of the time of first level $u$ crossing by the random process $\homV{s}-cs$, $s>0$, where…

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…

We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…

Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where basically $(X_k,k\ge 1)$ and $(\xi_y,y\in\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that $X_1$ is…

Consider a branching random walk, where the branching mechanism is governed by a Galton-Watson process, and the migration by a finite range symmetric irreducible random walk on the integer lattice $\mathbb{Z}^d$. Let $Z_n(z)$ be the number…

The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…

We study the asymptotic behaviour of the martingale ($\psi$ n (o)) n$\in$N associated with the Vertex Reinforced Jump Process (VRJP). We show that it is bounded in L p for every p > 1 on trees and uniformly integrable on Z d in all the…

The asymptotics of the probability that the self-intersection local time of a random walk on $\Z^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to…

Subordinating a random walk to a renewal process yields a continuous time random walk (CTRW) model for diffusion, including the possibility of anomalous diffusion. Transition densities of scaling limits of power law CTRWs have been shown to…

The site percolation problem is one of the core topics in statistical physics. Evaluation of the percolation threshold, which separates two phases (sometimes described as conducting and insulating), is useful for a range of problems from…

In this paper we study several aspects of the growth of a supercritical Galton-Watson process {Z_n:n\ge1}, and bring out some criticality phenomena determined by the Schroder constant. We develop the local limit theory of Z_n, that is, the…

We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of…

Let $(Z_n)$ be a supercritical branching process in an independent and identically distributed random environment $\xi$. We show the exact decay rate of the probability $\mathbb{P}(Z_n=j | Z_0 = k)$ as $n \to \infty$, for each $j \geq k,$…

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent…

In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…

We give a local central limit theorem for simple random walks on Z^d, including Gaussian error estimates. The detailed proof combines standard large deviation techniques with Cramer-Edgeworth expansions for lattice distributions.

For a subcritical Galton-Watson process $(\zeta_n)$, it is well known that under an $X \log X$ condition, the quotient $P(\zeta_n > 0)/ E\zeta_n$ has a finite positive limit. There is an analogous result for a (one-dimensional)…

The aim of this paper is to get asymptotic deviation bounds via a Large Deviation Principle (LDP) for cumulative processes also known as compound renewal processes or renewal-reward processes. These processes cumulate independent random…

The macroscopic study of hydrodynamic turbulence is equivalent, at an abstract level, to the microscopic study of a heat flow for a suitable mechanical system. Turbulent fluctuations (intermittency) then correspond to thermal fluctuations,…

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…