“Simple point process”的意思、由来-开放百科全书

词条

Simple point process

释义

Definition
Examples
Uniqueness
Literature

A simple point process is a special type of point process in probability theory. In simple point processes, every point is assigned the weight one.

Definition

Let be lcscH and let be the -algebra consisting of all relatively compact subsets of . A point process , interpreted as random measure on , is called a simple point process if it can be written as

for an index set and random elements . Here denotes the Dirac measure on the point .

Examples

Simple point processes include many important classes of point processes such as Poisson processes, Cox processes and binomial processes.

Uniqueness

If is a generating ring of then a simple point process is uniquely determined by its values on the sets . This means that two simple point processes and have the same distributions iff

Literature

{{cite book |last1=Kallenberg |first1=Olav |author-link1=Olav Kallenberg |year=2017 |title=Random Measures, Theory and Applications|location= Switzerland |publisher=Springer |doi= 10.1007/978-3-319-41598-7|isbn=978-3-319-41596-3}}
{{cite book |last1=Daley |first1=D.J. |last2= Vere-Jones | first2= D. |year=2003 |title=An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods,|location= New York |publisher=Springer |isbn=0-387-95541-0}}

1 : Point processes

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