Timeline for Total progeny of a Galton-Watson branching process - standard textbook question
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| Jan 27, 2017 at 19:27 | comment | added | esg | $r(s):=sg_Y(s)$ is the generating function of the total progeny in a GW-process with reproduction function $a_d(s)=q+ps^d$. (3) thus shows that the no. of successors of one individual in the GW-process with reproduction $b_d$ is distributed like the sum of the successors of $d$ independent GW-processes with reproduction $a_d$. In particular, the extinction probablity $r(1)$ of a GW-process with reproduction $b_d$ is the $d-$th power of the extinction probability of a GW-process with reproduction $a_d$. | |
| Jan 27, 2017 at 15:31 | vote | accept | Matjaž Krnc | ||
| Jan 27, 2017 at 15:30 | comment | added | Matjaž Krnc | Thank you for your answer! The additional details seem to be interesting - especially (3), once I digest it. Although the bounty went to Did (he was first) - I am accepting your answer because of an added value. Thanks! | |
| Jan 23, 2017 at 17:37 | history | answered | esg | CC BY-SA 3.0 |