Related papers: T. E. Harris and branching processes
This document is the Ph.D. thesis of Leonard Parker, submitted to Harvard University in 1966. Over the decades, several generations of physicists have been introduced to the concept of particle creation by gravitational fields, a phenomenon…
In this paper we prove that, under certain conditions, a strong law of large number holds for a class of branching particle systems $X$ corresponding to the parameters $(Y,\beta,\psi)$, where $Y$ is a Hunt process and $\psi$ is the…
We consider empirical processes generated by strictly stationary sequences of associated random variables. S. Louhichi established an invariance principle for such processes, assuming that the covariance function decays rapidly enough. We…
Following the pivotal work of Sevastyanov, who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes under different types of branching and immigration…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
The hard edge Pearcey process is universal in random matrix theory and many other stochastic models. This paper deals with the gap probability for the thinned/unthinned hard edge Pearcey process over the interval $(0,s)$ by working on the…
This paper synthesises the existing research on the dynamics of innovation diffusion, with a focus on Bass-type models and their extensions. The theoretical foundation of innovation diffusion proposed by Rogers (1962) and the seminal work…
This note considers the notion of divergence-preserving branching bisimilarity. It briefly surveys results pertaining to the notion that have been obtained in the past one-and-a-half decade, discusses its role in the study of expressiveness…
This is an epistemological approach to errors in both inference and risk management, leading to necessary structural properties for the probability distribution. Many mechanisms have been used to show the emergence of fat tails. Here we…
The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of…
The paper is devoted to the contribution in the Probability Theory of the well-known Soviet mathematician Alexander Yakovlevich Khintchine (1894-1959). Several of his results are described, in particular those fundamental results on the…
It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
Professor Jayanta Kumar Ghosh has contributed massively to various areas of Statistics over the last five decades. Here, we survey some of his most important contributions. In roughly chronological order, we discuss his major results in the…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
A branching L\'evy process can be seen as the continuous-time version of a branching random walk. It describes a particle system on the real line in which particles move and reproduce independently in a Poissonian manner. Just as for L\'evy…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…