相关论文: T. E. Harris and branching processes

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.

The book "Continuous-Time Markov Chains" by W. J. Anderson collects a large part of the development in the past thirty years. It is now a popular reference for the researchers on this subject or related fields. Unfortunately, due to a…

Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…

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 wide applications in finance, neuroscience and many other…

We first present an introduction to the theory of hard exclusive processes. We then illustrate this theory by a few selected examples. The last part is devoted to the most recent developments in the asymptotical energy limit.

The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…

Laplace's views on randomness and determinism. The paper was written for "Cahiers rationalistes" and addresses a rather wide audience. It contains large quotations of Laplace, most of them coming from his introduction to the book…

In my book ``Large Scale Dynamics of Interacting Particles'' [S] I refer to an unpublished note from early 1985 on the BBGKY hierarchy for hard spheres. My main point there was to provide a direct probabilistic proof for the time-integrated…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…

The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…

Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this paper, we extend the multi-type branching process method developed in Keating et…

Branching processes are widely used to model phenomena from networks to neuronal avalanching. In a large class of continuous-time branching processes, we study the temporal scaling of the moments of the instant population size, the survival…

Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme…

Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them and also copies a fraction of their references (cond-mat/0305150). The model was stimulated by our discovery that a…

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…

In 1746 Euler publishes E88 -- Nova theoria lucis et colorum (A new theory of light and colors) in five chapters. This is an annotated translation of Chapter II - De formatione ac propagatione pulsuum (On the formation and propagation of…