Related papers: On limit theorems for functional autoregressive pr…

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…

We consider the branching process in random environment $\{Z_n\}_{n\geq 0}$, which is a~population growth process where individuals reproduce independently of each other with the reproduction law randomly picked at each generation. We focus…

We observe a multilinearity preserving property of conditional expectation for infinite dimensional independent increment processes defined on some abstract Banach space $B$. It is similar in nature to the polynomial preserving property…

The aim of this paper is to prove the strong law of large numbers (SLLN) as well as the central limit theorem (CLT) for a class of vector-valued stochastic processes which arise as solutions of the stochastic evolution inclusion…

In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…

We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

This thesis addresses Pour-El and Richards' fourth question from their book "Computability in analysis and physics", concerning the relation between higher order recursion theory and computability in analysis. Among other things it is shown…

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between…

In this paper we establish a weak and a strong law of large numbers for supercritical superprocesses with general non-local branching mechanisms. Our results complement earlier results obtained for superprocesses with only local branching.…

We prove weak convergence on the Skorokhod space of Galton-Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot…

The paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on $\mathbb{Z}$. This result appears as an extension of the invariance principal theorem for classical random walks on $\mathbb{Z}$ or…

We extend classical results about the convergence of nearly unstable AR(p) processes to the infinite order case. To do so, we proceed as in recent works about Hawkes processes by using limit theorems for some well chosen geometric sums. We…

In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…

We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement to those presented previously in the literature. As an…

In this paper, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-Chervonenkis properties.

The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in…

We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on…