Point process notation: Difference between revisions

Revision as of 09:36, 12 October 2013

Revision as of 10:23, 12 October 2013

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</ref><ref name="moller2003statistical"> J. Moller and R. P. Waagepetersen. ''Statistical inference and simulation for spatial point processes''. CRC Press, 2003.

</ref><ref name="stoyan1995stochastic"/>, for example <math> \Phi</math>, and if <math>the point \Phi</math>process is considered as a random set, then the corresponding notation<ref name="stoyan1995stochastic"/>:

:<math> x\in \Phi, </math>

n

is used to denote that a random point <math> x</math> belongs to or is an [[Element (mathematics)|element]] of the point process <math> \Phi</math>. The theory of random sets can be applied to point processes owing to this interpretation. These two interpretations have resulted in a point process being written as:

:<math> \{x_1, x_2,\dots \}=\{x\}_i</math>,