Related papers: Finitary isomorphisms of renewal point processes a…

A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…

We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that…

Permanental processes can be viewed as a generalisation of squared centered Gaussian processes. We develop in this paper two main subjects. The first one analyses the connections of these processes with the local times of general Markov…

It is shown that for a non-decreasing self-similar stochastic process $T$ with independent increments, the range of $T$ forms a Poisson point process with $\sigma$-finite intensity if and only if the one-dimensional distribution of $T(1)$…

Extremal clusters of stationary processes with long memory can be quite intricate. For certain stationary infinitely divisible processes with subexponential tails, including both power-like tails and certain lighter tails, e.g.…

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form…

Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…

We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily…

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 show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…

Consider two independent Poisson point processes of unit intensity in the Euclidean space of dimension $d$ at least 3. We construct a perfect matching between the two point sets that is a factor (i.e., an equivariant measurable function of…

We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal…

Given a sequence of i.i.d. random functions $\Psi_{n}:\mathbb{R}\to\mathbb{R}$, $n\in\mathbb{N}$, we consider the iterated function system and Markov chain which is recursively defined by $X_{0}^{x}:=x$ and…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of…

We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property…

We give general sufficient conditions to prove the convergence of marked point processes that keep record of the occurrence of rare events and of their impact for non-autonomous dynamical systems. We apply the results to sequential…

If the step distribution in a renewal process has finite mean and regularly varying tail with index -{\alpha}, 1<{\alpha}<2, the first two terms in the asymptotic expansion of the renewal function have been known for many years. Here we…

Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the…

We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…