相关论文: Correlated Poisson processes and self-decomposable…

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of…

We consider two fractional versions of a family of nonnegative integer valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As…

Commonalities and differences in correlation analysis in terms of phase space, conditioning and uncorrelatedness are discussed. The Poisson process is not generally appropriate as reference distribution for normalisation and cumulants, so…

After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because…

Emergent behaviors occur in a vast array of systems across many scales, and are of fundamental physical importance because of the intrinsic difficulty in linking microscopic system properties to macroscopic behaviors. Here we study the…

We construct an asymptotic expansion in powers of the coupling constant directly of the cross-section for pair production and decay of fundamental unstable particles. The resonant and kinematic singularities arising in the expansion we…

This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its…

In the paper we consider time-changed Poisson processes where the time is expressed by compound Poisson-Gamma subordinators $G(N(t))$ and derive the expressions for their hitting times. We also study the time-changed Poisson processes where…

This paper analyses a system subject to multiple dependent degradation processes. Degradation processes start at random times following a non homogeneous Poisson process and next dependently propagate. The growth of these degradation…

For $N\in\mathbb{N}$, let $\pi_N$ be the law of the number of fixed points of a random permutation of $\{1, 2, ..., N\}$. Let $\mathcal{P}$ be a Poisson law of parameter 1.A classical result shows that $\pi_N$ converges to $\mathcal{P}$ for…

Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood…

We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the…

We study pivotal decomposition schemes and investigate classes of pivotally decomposable operations. We provide sufficient conditions on pivotal operations that guarantee that the corresponding classes of pivotally decomposable operations…

A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained. Some…

Based on the high statistics data from the pp -> ppX reaction measured by the COSY-11 collaboration [1] we have derived a two-proton correlation function for the production of the ppeta and pp+pions systems. The measured correlation…

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

This is survey of some recent results connecting random matrices, non-colliding processes and queues.

The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…

We give necessary and sufficient conditions guaranteeing that the coupling for L\'evy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process…