相关论文: Limits of renewal processes and Pitman-Yor distrib…

We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space…

We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the…

We consider a system of $N$ particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the…

We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

In this paper we prove that under weak conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p-variation norms, greedy time…

When the distribution of the inter-arrival times of a renewal process is a mixture of geometric laws, we prove that the renewal function of the process is given by the moments of a probability measure which is explicitly related to the…

This article considers the statistical properties of L\'evy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply.…

We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…

Consider a sequence (Z_n,Z_n^M) of bivariate L\'evy processes, such that Z_n is a spectrally positive L\'evy process with finite variation, and Z_n^M is the counting process of marks in {0,1} carried by the jumps of Z_n. The study of these…

Stick-breaking has a long history and is one of the most popular procedures for constructing random discrete distributions in Statistics and Machine Learning. In particular, due to their intuitive construction and computational tractability…

We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…

Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming-Viot type particle system with…

This paper deals with the large deviations behavior of a stochastic process called thinned Levy process. This process appeared recently as a stochastic-process limit in the context of critical inhomogeneous random graphs. The process has a…

A controlled branching process (CBP) is a modification of the standard Bienaym\'e-Galton-Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random…

We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…

We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first…