71 citations · 558 across the 67 of their papers we have counts for
24 papers · 1 filter
Fluctuations and moderate deviations for the mean fields of Hawkes processes
Fuqing Gao, Yunshi Gao, Lingjiong Zhu
The Hawkes process is a counting process that has self- and mutually-exciting features with many applications in various fields. In recent years, there have been many interests in…
Large deviations for the mean-field limit of Hawkes processes
Fuqing Gao, Lingjiong Zhu
Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various…
Affine Point Processes: Refinements to Large-Time Asymptotics
Xuefeng Gao, Lingjiong Zhu
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, w…
Some asymptotic results for nonlinear Hawkes processes
Fuqing Gao, Lingjiong Zhu
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks,…
Precise deviations for Hawkes processes
Fuqing Gao, Lingjiong Zhu
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks,…
Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues
Xuefeng Gao, Lingjiong Zhu
A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensi…
Large deviations and applications for Markovian Hawkes processes with a large initial intensity
Xuefeng Gao, Lingjiong Zhu
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has…
Limit theorems for Markovian Hawkes processes with a large initial intensity
Xuefeng Gao, Lingjiong Zhu
Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applic…
On the growth rate of a linear stochastic recursion with Markovian dependence
Dan Pirjol, Lingjiong Zhu
We consider the linear stochastic recursion where the multipliers are random and have Markovian dependence given by the exponential of a standard…
Asymptotics for a Class of Self-Exciting Point Processes
Tzu-Wei Yang, Lingjiong Zhu
In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs…
Asymptotics for Sparse Exponential Random Graph Models
Mei Yin, Lingjiong Zhu
We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean a…
Asymptotic Structure of Constrained Exponential Random Graph Models
Lingjiong Zhu
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that the…
Asymptotic structure and singularities in constrained directed graphs
David Aristoff, Lingjiong Zhu
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward -stars. Our models are close cousins of exponential random graph…
On the phase transition curve in a directed exponential random graph model
David Aristoff, Lingjiong Zhu
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the n…
On the Hawkes Process with Different Exciting Functions
Behzad Mehrdad, Lingjiong Zhu
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process i…
Moderate and Large Deviations for the Erdős-Kac Theorem
Behzad Mehrdad, Lingjiong Zhu
The Erdős-Kac theorem is a celebrated result in number theory which says that the number of distinct prime factors of a uniformly chosen random integer satisfies a central limit th…
Limit Theorems for Empirical Density of Greatest Common Divisors
Behzad Mehrdad, Lingjiong Zhu
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In thi…
Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps
Lingjiong Zhu
In this paper, we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross proc…
Nonlinear Hawkes Processes
Lingjiong Zhu
The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-excitin…
The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias
Behzad Mehrdad, Sanchayan Sen, Lingjiong Zhu
Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions and (GW and GW) where and are supported on…
Limit Theorems for Marked Hawkes Processes with Application to a Risk Model
Dmytro Karabash, Lingjiong Zhu
This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi…
Central Limit Theorem for Nonlinear Hawkes Processes
Lingjiong Zhu
Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance and man…
Large deviations for Markovian nonlinear Hawkes processes
Lingjiong Zhu
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has…
Process-Level Large Deviations for Nonlinear Hawkes Point Processes
Lingjiong Zhu
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a r…