Related papers: Process-Level Large Deviations for Nonlinear Hawke…

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional…

We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a…

We consider a non-stationary Cox-Ingersoll-Ross process. We establish a sharp large deviation principle for the maximum likelihood estimator of its drift parameter.

We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each…

We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results around equilibrium solutions, under some local subcritical…

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…

Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding…

In this paper we consider multivariate Hawkes processes with baseline hazard and kernel functions that depend on time. This defines a class of locally stationary processes. We discuss estimation of the time-dependent baseline hazard and…

A uniform law of large numbers and a central limit theorem are established via a martingale approach for a univariate Hawkes process with immigration given by a renewal process. The results are obtained for renewal processes with absolutely…

The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled…

We prove large deviation principles (LDP) for the invariant measures of the multiclass totally asymmetric simple exclusion process (TASEP) and the multiclass Hammersely-Aldous-Diaconis (HAD) process on a torus. The proof is based on a…

The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where…

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…

Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this…

In this work, we study large deviation properties of the covariance process in fully connected Gaussian deep neural networks. More precisely, we establish a large deviation principle (LDP) for the covariance process in a functional…

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…

In this paper, we study the large deviation principle (LDP) for two types (Type I and Type II) of multiplicative Ising models. For Types I and II, the explicit formulas for the free energy functions and the associated rate functions are…