Poisson random measure information

be some measure space with σ {\displaystyle \sigma } -finite measure μ {\displaystyle \mu } . The Poisson random measure with intensity measure μ {\displaystyle...

independently of one another. The Poisson point process is also called a Poisson random measure, Poisson random point field and Poisson point field. When the process...

point processes such as Poisson point processes and Cox processes. Random measures can be defined as transition kernels or as random elements. Both definitions...

conditions are true, then k is a Poisson random variable, and the distribution of k is a Poisson distribution. The Poisson distribution is also the limit...

theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise...

A compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of...

interpreted as a random set or a random counting measure, instead of a stochastic process. In this setting, the Poisson process, also called the Poisson point process...

Poisson clumping, or Poisson bursts, is a phenomenon where random events may appear to occur in clusters, clumps, or bursts. Poisson clumping is named...

{\displaystyle X=x} is a Poisson process on S {\displaystyle S} with intensity measure x μ {\displaystyle x\mu } . Mixed Poisson processes are doubly stochastic...

statistics, Poisson regression is a generalized linear model form of regression analysis used to model count data and contingency tables. Poisson regression...

Random compact set Random element Random function Random measure Random number generator Random variate Random vector Randomness Stochastic process Relationships...

absolutely continuous measures see absolutely continuous measure. In the measure-theoretic formalization of probability theory, a random variable is defined...

representation theorem Azuma's inequality Wald's equation Poisson process Poisson random measure Population process Process with independent increments Progressively...

{\bar {N}}} is an l {\displaystyle l} -dimensional compensated Poisson random measure, b : R k → R k {\displaystyle b:\mathbb {R} ^{k}\to \mathbb {R}...

increments and independent S-increments of random measures plays an important role in the characterization of Poisson point process and infinite divisibility...

distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently...

towards the Poisson distribution as the number of trials goes to infinity while the product np converges to a finite limit. Therefore, the Poisson distribution...

Non-homogeneous Poisson process / (U:D) Point process / (U:D) Poisson process / (U:D) Poisson random measure / (U:D) Random measure / (U:D) Renewal theory /...

tessellations, random geometric graphs, and Boolean models. Empirical measure Random measure Point process notation Point process operation Poisson process Renewal...

the Poisson boundary is a measure space associated to a random walk. It is an object designed to encode the asymptotic behaviour of the random walk,...

of the random measure. A Poisson point process, interpreted as a random measure, is for example uniquely determined by its intensity measure. Let ζ {\displaystyle...

mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies measure properties such as countable...

mathematics, a random walk, sometimes known as a drunkard's walk, is a random process that describes a path that consists of a succession of random steps on...

{\displaystyle {\mathcal {L}}(\eta \mid \xi =\mu )} is a Poisson process with intensity measure μ {\displaystyle \mu } . Here, L ( η ∣ ξ = μ ) {\displaystyle...

Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature...

from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning...