scholarly journals KPZ formula for log-infinitely divisible multifractal random measures

2011 ◽  
Vol 15 ◽  
pp. 358-371 ◽  
Author(s):  
Rémi Rhodes ◽  
Vincent Vargas
Keyword(s):  
Random Measures ◽  
Infinitely Divisible

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 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.

Rarefactions of compound point processes

1984 ◽  
Vol 21 (4) ◽  
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.

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