Related papers: Limit theorems for additive functionals of random …

For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis.…

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…

We consider transient nearest-neighbor random walks in random environment on Z. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level n, around…

We consider a real random walk S_n = X_1 + ... + X_n attracted (without centering) to the normal law: this means that for a suitable norming sequence a_n we have the weak convergence S_n / a_n --> f(x) dx, where f(x) is the standard normal…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

We derive asymptotics of moments and identify limiting distributions, under the random permutation model on m-ary search trees, for functionals that satisfy recurrence relations of a simple additive form. Many important functionals…

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

This paper explores the joint behaviour of the summands of a random walk when their mean value goes to infinity as its length increases. It is proved that all the summands must share the same value, which extends previous results in the…

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…

Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabilities at a given time and at a given site are made…

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step…

Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…

We present a Darboux-Wiener type lemma and apply it to obtain an exact asymptotic for the variance of the self-intersection of one and two-dimensional random walks. As a corollary, we obtain a central limit theorem for random walk in random…

We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…

In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $\sigma$--record…

We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence of moments for first-passage and last-exit times. In our…

We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is…

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of…