scholarly journals A constructive approach to the law equivalence of infinitely divisible random measures

1994 ◽  
Vol 70 (9) ◽  
pp. 282-285
Author(s):  
Kazuyuki Inoue
Keyword(s):  
Constructive Approach ◽  
Random Measures ◽  
Infinitely Divisible ◽  
The Law

Rarefactions of compound point processes

1984 ◽  
Vol 21 (04) ◽  
pp. 710-719
Author(s):  
Richard F. Serfozo
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Classical Result ◽  
Point Processes ◽  
Rare Events ◽  
Random Measure ◽  
Bernoulli Trials ◽  
Random Measures ◽  
Infinitely Divisible ◽  
Independent Increments

The Poisson process is regarded as a point process of rare events because of the classical result that the number of successes in a sequence of Bernoulli trials is asymptotically Poisson as the probability of a success tends to 0. It is shown that this rareness property of the Poisson process is characteristic of any infinitely divisible point process or random measure with independent increments. These processes and measures arise as limits of certain rarefactions of compound point processes: purely atomic random measures with uniformly null atom sizes. Examples include thinnings and partitions of point processes.

scholarly journals A discrete multivariate distribution resulting from the law of small numbers

2006 ◽  
Vol 43 (03) ◽  
pp. 852-866 ◽  
Author(s):  
Nobuaki Hoshino
Keyword(s):  
Count Data ◽  
Exponential Family ◽  
Divisible Distribution ◽  
Multivariate Distribution ◽  
Inverse Gaussian ◽  
Real Numbers ◽  
Infinitely Divisible ◽  
The Law ◽  
Positive Integers ◽  
New Distribution

In the present article we derive a new discrete multivariate distribution using a limiting argument that is essentially the same as the law of small numbers. The distribution derived belongs to an exponential family, and randomly partitions positive integers. The facts shown about the distribution are useful in many fields of application involved with count data. The derivation parallels that of the Ewens distribution from the gamma distribution, and the new distribution is produced from the inverse Gaussian distribution. The method employed is regarded as the discretization of an infinitely divisible distribution over nonnegative real numbers.

scholarly journals Bartlett spectrum and mixing properties of infinitely divisible random measures

2007 ◽  
Vol 39 (04) ◽  
pp. 893-897
Author(s):  
Emmanuel Roy
Keyword(s):  
Gaussian Process ◽  
Spectral Measure ◽  
Random Measure ◽  
Stationary Gaussian Process ◽  
Random Measures ◽  
Infinitely Divisible ◽  
Weak Mixing ◽  
Mixing Properties

We prove that the Bartlett spectrum of a stationary, infinitely divisible (ID) random measure determines ergodicity, weak mixing, and mixing. In this context, the Bartlett spectrum plays the same role as the spectral measure of a stationary Gaussian process.

Sign in / Sign up

Export Citation Format

Share Document