Function-indexed empirical processes based on an infinite source Poisson transmission stream

群索引无限可分平稳过程的遍历性与弱混合性

Ergodicity and weak mixing for group-indexed infinitely divisible stationary processes

研究群索引无限可分平稳过程，通过对概率可分平稳过程进行随机连续扩展构造，将问题简化，证明了遍历无限可分平稳过程是弱混合的，揭示遍历性蕴含弱混合性是无限可分性固有属性，去除群结构假设。

First Steps Towards an Imprecise Poisson Process

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate interval and let it characterise two nested sets of stochastic processes. We call these two sets of stochastic process imprecise Poisson processes, explain why this is justified, and study the corresponding lower and upper (conditional) expectations. Besides a general theoretical framework, we also provide practical methods to compute lower and …

Poisson 可表示过程

Poisson Representable Processes

受 Sznitman 交叠过程启发，本文研究由集合族上 Poisson 过程构造的取值 $\{0,1\}$ 的可表示过程，给出了判定其可表示性的条件，并证明了 Markov 链、更新过程等的可表示性及 Ising、Curie-Weiss 等模型的不可表示性。

双参数Poisson-Dirichlet分布和Pitman-Yor过程的动力学模型

Dynamical models for the two-parameter Poisson-Dirichlet distribution and the Pitman-Yor process

本文引入并研究了一族与Pitman-Yor过程和双参数Poisson-Dirichlet分布相关的扩散过程，通过Dirichlet形式构造，并揭示了多样性指数在种群演化中的关键作用。

WARM percolation on a regular tree in the strong reinforcement regime

We consider a class of reinforcement processes, called WARMs, on tree graphs. These processes involve a parameter $α$ which governs the strength of the reinforcement, and a collection of Poisson processes indexed by the vertices of the graph. It has recently been proved that for any fixed bounded degree graph with Poisson firing rates that are uniformly bounded above, in the very strong reinforcement regime ($α\gg 1$ sufficiently large depending on the maximal degree), the set of edges that "survive" (i.e. that are reinforced infinitely often by the process) has only finite connected component…

Upper bounds for spatial point process approximations

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed processes behave approximately like Poisson processes for large T. In this article, under very similar assumptions, explicit upper bounds are given for the d_2-distance between the corresponding point process distributions. A number of related results, and applications to kernel density estimation and long range dependence testing are also presented. The main…

泊松计数过程与带有偏移的线性移动边界的第一通过问题

A first passage problem for a Poisson counting process with a linear moving boundary

本文研究泊松计数过程与线性移动边界的第一通过时间问题，通过直接时域方法和拉普拉斯域方法统一分析，推导出亚临界区域的大偏差函数和任意偏移下的条件均值第一通过时间的闭式表达式。

A new encoding of coalescent processes. Applications to the additive and multiplicative cases

We revisit the discrete additive and multiplicative coalescents, starting with $n$ particles with unit mass. These cases are known to be related to some "combinatorial coalescent processes": a time reversal of a fragmentation of Cayley trees or a parking scheme in the additive case, and the random graph process $(G(n,p))_p$ in the multiplicative case. Time being fixed, encoding these combinatorial objects in real-valued processes indexed by the line is the key to describing the asymptotic behaviour of the masses as $n\to +\infty$. We propose to use the Prim order on the vertices instead of the…

The generalized join the shortest orbit queue system: Stability, exact tail asymptotics and stationary approximations

We introduce the \textit{generalized join the shortest queue model with retrials} and two infinite capacity orbit queues. Three independent Poisson streams of jobs, namely a \textit{smart}, and two \textit{dedicated} streams, flow into a single server system, which can hold at most one job. Arriving jobs that find the server occupied are routed to the orbits as follows: Blocked jobs from the \textit{smart} stream are routed to the shortest orbit queue, and in case of a tie, they choose an orbit randomly. Blocked jobs from the \textit{dedicated} streams are routed directly to their orbits. Orbi…

A Model of Distributed Disorders Detection

The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed detection system. The multivariate renewal process can be seen as the sequence of random vectors, where parts of its coordinates are holding times, others are the size of jumps and the index of stream, at which the new event appears. It is assumed that at each stream two kinds of changes are possible: in the holding time or in the size of jumps distribution. …