Representations of Invariant Measures on Multitype Galton-Watson Processes
Representations of Invariant Measures on Multitype Galton-Watson Processes
We show that there is a one-to-one correspondence between invariant measures for the noncritical multitype Galton-Watson process and invariant measures for the single type process with a linear offspring probability generating function. Two corollaries emerge as simple applications, the first being Spitzer's Martin boundary representation, the second giving the asymptotic …