Related papers: On Compound Poisson Processes Arising in Change-Po…
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
We study point processes that consist of certain centers of point tuples of an underlying Poisson process. Such processes arise in stochastic geometry in the study of exceedances of various functionals describing geometric properties of the…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…
Under mild assumptions the equivalence of the mixed Poisson process with mixing parameter a real-valued random variable to the one with mixing distribution as well as to the mixed Poisson process in the sense of Huang is obtained, and a…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to…
We present a new, analytic, Poisson likelihood derived, technique to account for the statistical uncertainties inherent in simulation samples of limited size. This method has better coverage properties than other techniques, is valid for…
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…
Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…
The aim of the present work is to show that the results obtained earlier on the approximation of distributions of sums of independent terms by the accompanying compound Poisson laws may be interpreted as rather sharp quantitative estimates…
We construct a family of processes, from a single Poisson process, that converges in law to a complex Brownian motion. Moreover, we find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly…
We detect the parameter sensitivities of bond pricing which is driven by a Brownian motion and a compound Poisson process as the discontinuous case in credit risk research. The strict mathematical deductions are given theoretically due to…
We establish Poisson and compound Poisson approximations for stabilizing statistics of $\beta$-mixing point processes and give explicit rates of convergence. Our findings are based on a general estimate of the total variation distance of a…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…