Related papers: On a central limit theorem in renewal theory

A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at…

We establish a central limit theorem for counting large continued fraction digits $(a_n)$, i.e. we count occurrences $\{a_n>b_n\}$, where $(b_n)$ is a sequence of positive integers. Our result improves a similar result by Philipp which…

Let $(X_i,i\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\infty$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq…

Consider the map $(x, y) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-1-\alpha}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. The parameter value $\alpha = 1$ is related…

We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…

We prove quenched versions of a central limit theorem, a large deviations principle as well as a local central limit theorem for expanding on average cocycles. This is achieved by building an appropriate modification of the spectral method…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated…

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate N times alpha,choose L queues uniformly, and join the shortest one. The stability condition is alpha strictly less than beta. We study in…

We prove three strong approximation theorems for the `supermarket' or `join the shortest queue' model -- a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly.…

Using Stein's method, we prove an abstract result that yields multivariate central limit theorems with a rate of convergence for time-dependent dynamical systems. As examples we study a model of expanding circle maps and a quasistatic…

We consider a supercritical general branching population where the lifetimes of individuals are i.i.d. with arbitrary distribution and each individual gives birth to new individuals at Poisson times independently from each others. The…

In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…

Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b \ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the…

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…

We establish the central limit theorem for the number of groups at the equilibrium of a coagulation-fragmentation process given by a parameter function with polynomial rate of growth. The result obtained is compared with the one for random…

In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…