Exact distribution of kin number in multitype Galton-Watson process

1986 ◽  
pp. 397-405 ◽  
Author(s):  
A. Joffe ◽  
W. A. O’N. Waugh
Keyword(s):  
Exact Distribution ◽  
Watson Process

On the age distribution of a Markov chain

1978 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Anthony G. Pakes
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Limit Theorems ◽  
Age Distribution ◽  
Weak Limit ◽  
Absorbing State ◽  
Absorbing Markov Chain ◽  
Continuous Random Walk ◽  
A Chain ◽  
Watson Process

This paper develops the notion of the limiting age of an absorbing Markov chain, conditional on the present state. Chains with a single absorbing state {0} are considered and with such a chain can be associated a return chain, obtained by restarting the original chain at a fixed state after each absorption. The limiting age, A(j), is the weak limit of the time given Xn = j (n → ∞).A criterion for the existence of this limit is given and this is shown to be fulfilled in the case of the return chains constructed from the Galton–Watson process and the left-continuous random walk. Limit theorems for A (J) (J → ∞) are given for these examples.

On the Controlled Galton-Watson Process with Random Control Function

2004 ◽  
Vol 121 (5) ◽  
pp. 2629-2635 ◽  
Author(s):  
M. González ◽  
M. Molina ◽  
I. del Puerto
Keyword(s):  
Control Function ◽  
Watson Process ◽  
Random Control

Markov processes associated with critical Galton-Watson processes with application to extinction probabilities

1976 ◽  
Vol 8 (2) ◽  
pp. 278-295 ◽  
Author(s):  
Michael Sze
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Continuous Process ◽  
Regularly Varying Functions ◽  
Original Process ◽  
Additional Information ◽  
Embedding Technique ◽  
Extinction Probabilities ◽  
Watson Process ◽  
The Given

As an alternative to the embedding technique of T. E. Harris, S. Karlin and J. McGregor, we show that given a critical Galton–Watson process satisfying some mild assumptions, we can always construct a continuous-time Markov branching process having the same asymptotic behaviour as the given process. Thus, via the associated continuous process, additional information about the original process is obtained. We apply this technique to the study of extinction probabilities of a critical Galton–Watson process, and provide estimates for the extinction probabilities by regularly varying functions.

The Galton-Watson Process: Probabilistic Methods

1983 ◽  
pp. 17-54
Author(s):  
Søren Asmussen ◽  
Heinrich Hering
Keyword(s):  
Probabilistic Methods ◽  
Watson Process
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