Abstract
A random variable Y is branching stable (B-stable) for a nonnegative integer-valued random variable J with E(J)>1 if Y*J∿cY for some scalar c, where Y*J is the sum of J independent copies of Y. We explore some aspects of this notion of stability and show that, for any Y0 with finite nonzero mean, if we define Yn+1=Yn*J/E(J) then the sequence Yn converges in law to a random variable Y∞ that is B-stable for J. Also Y∞ is the unique B-stable law with mean E(Y0). We also present results relating to random variables Y0 with zero means and infinite means. The notion of B-stability arose in a scheme for cataloguing a large network of computers.
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