Related papers: Limit theorems for Hawkes processes including inhi…
In this article, we fill a gap in the literature regarding quantitative functional central limit theorems (qfCLT) for Hawkes processes by providing an upper bound for the convergence of a nearly unstable Hawkes process toward a…
In this note we re-visit the fundamental question of the strong law of large numbers and central limit theorem for processes in continuous time with conditional stationary and independent increments. For convenience we refer to them as…
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process…
This continues work started in part I on a general branching-within-branching model for host-parasite co-evolution. Here we focus on asymptotic results for relevant processes in the case when parasites survive. In particular, limit theorems…
Hawkes processes are a self-exciting stochastic process used to describe phenomena whereby past events increase the probability of the occurrence of future events. This work presents a flexible approach for modelling a variant of these,…
The persistent homology of a stationary point process on ${\bf R}^N$ is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops,…
We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…
We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…
We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers,…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
Interval-censored data solely records the aggregated counts of events during specific time intervals - such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors - and not the exact…
We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
In the present work we derive a Central Limit Theorem for sequences of Hilbert-valued Piecewise Deterministic Markov process models and their global fluctuations around their deterministic limit identified by the Law of Large Numbers. We…
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…