scholarly journals Poisson representation of strict regular step filtrations

1986 ◽  
pp. 1-27 ◽  
Author(s):  
F. B. Knight
Keyword(s):  
Poisson Representation

scholarly journals Nonlinear diffusion and hyperuniformity from Poisson representation in systems with interaction mediated dynamics

2019 ◽  
Vol 21 (12) ◽  
pp. 123048 ◽  
Author(s):  
Thibault Bertrand ◽  
Didier Chatenay ◽  
Raphaël Voituriez
Keyword(s):  
Nonlinear Diffusion ◽  
Poisson Representation

scholarly journals Poisson Representation of a Ewens Fragmentation Process

2007 ◽  
Vol 16 (6) ◽  
pp. 819-827 ◽  
Author(s):  
ALEXANDER GNEDIN ◽  
JIM PITMAN
Keyword(s):  
Poisson Process ◽  
Explicit Construction ◽  
Unit Interval ◽  
Fragmentation Process ◽  
Ewens Sampling Formula ◽  
Uniform Sampling ◽  
Sampling Formula ◽  
Mass Fragmentation ◽  
Poisson Representation

A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n] = 1,. . .,nat time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, asnvaries. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx−1dx on/mathbbR+, arranged to beintensifying as θ increases.

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