Point process notation: Difference between revisions

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Latest revision as of 14:13, 3 February 2025

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{{Short description|Mathematical notation used in probability and statistics}}

{{ProbabilityTopics}}

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==Interpretation of point processes==

The notation, as well as the terminology, of point processes depends on their setting and interpretation as mathematical objects which under certain assumptions can be interpreted as random [[sequences]] of points, random [[Set (mathematics)|sets]] of points or random [[random counting measure]]s.<ref name="stoyan1995stochastic"/>

===Random sequences of points===

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

where which puts an emphasis on the interpretation of <math> {N}</math> being a random counting measure. An alternative integration notation may be used to write this integral as:

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