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The Martin Entrance Boundary of the Galton-Watson Process
 

Summary: 1
The Martin Entrance Boundary of the
Galton-Watson Process
Gerold Alsmeyer
Institut f¨ur Mathematische Statistik
Fachbereich Mathematik
Westf¨alische Wilhelms-Universit¨at M¨unster
Einsteinstraße 62
D-48149 M¨unster, Germany
Uwe R¨osler
Mathematisches Seminar
Christian-Albrechts-Universit¨at Kiel
Ludewig-Meyn-Straße 4
D-24098 Kiel, Germany
The paper provides a complete description of the Martin entrance bound-
ary and its minimal elements for a Galton-Watson process (Zn)n0.
Since this is easily done and known for critical processes, we deal with
the noncritical case which in turn can be reduced to the subcritical one.
The Martin entrance boundary consists of all quasi-invariant Radon
measures. The minimal Martin entrance boundary is isomorphic to

  

Source: Alsmeyer, Gerold - Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster

 

Collections: Mathematics