Multitype Bienayme-Galton-Watson processes escaping extinction.

Content Provider	Semantic Scholar
Author	Sagitov, Serik Serra, Maria Conceição
Copyright Year	2009
Abstract	In the framework of a multitype Bienayme–Galton–Watson (BGW) process, the event that the daughter’s type differs from the mother’s type can be viewed as a mutation event. Assuming that mutations are rare, we study a situation where all types except one produce on average less than one offspring. We establish a neat asymptotic structure for the BGW process escaping extinction due to a sequence of mutations toward the supercritical type. Our asymptotic analysis is performed by letting mutation probabilities tend to 0. The limit process, conditional on escaping extinction, is another BGW process with an enriched set of types, allowing us to delineate a stem lineage of particles that leads toward the escape event. The stem lineage can be described by a simple Markov chain on the set of particle types. The total time to escape becomes a sum of a random number of independent, geometrically distributed times spent at intermediate types.
Starting Page	225
Ending Page	246
Page Count	22
File Format	PDF HTM / HTML
DOI	10.1239/aap/1240319583
Alternate Webpage(s)	http://www.math.chalmers.se/~serik/Papers/SagitovSerra.pdf
Alternate Webpage(s)	https://doi.org/10.1239/aap%2F1240319583
Volume Number	41
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article