Kenji Kurata, Nariyuki Minami
The Equivalence of Two Constructions of Galton-Watson Processes
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ABSTRACT.  In most textbooks on branching processes, the Galton-Watson process is 
defined as an integer valued Markov chain with a special kind of transition probability, somtimes supplemented with an intuitive description of random family trees. A precise construction of the Galton-Watson process on the space of trees was first given by R. Otter in 1949, and later independently by J. Neveu in 1986. In this note, we show that these two constructions are actually equivalent.