Point process notation: Difference between revisions

Revision as of 14:38, 13 December 2019

Revision as of 09:02, 23 March 2020

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or, equivalently, with integration notation as:

:<math> \int_{\textbf{NR}^d} f(x) {N}(dx) </math>

where <math>which \textbf{N}</math> is the [[Sample space|space]] of all possible counting measures, hence puttingputs an emphasis on the interpretation of <math> {N}</math> asbeing a random counting measure. An alternative integration notation may be used to write this integral as:

:<math> \int_{\textbf{NR}^d} f \, d{N} </math>

The dual interpretation of point processes is illustrated when writing the number of <math> {N}</math> points in a set <math> B</math> as: