Multitype branching processes in random environments with not strictly positive expectation matrices
Abstract
It is well known that under some conditions the almost sure survival probability of a multitype branching process in random environment is positive if the Lyapunov exponent corresponding to the expectation matrices is positive, and zero if the Lyapunov exponent is negative. The goal of this note is to establish similar results when certain positivity conditions on the expectation matrices are not met. One application of such a result is to classify the positivity of Lebesgue measure of certain overlapping random self-similar sets.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Mathematical Dynamics and Fractals
advanced mathematical theories
Publication details
- Journal / source
- Bernoulli
- Volume
- 32
- Issue
- 2
- Pages
- 1328–1355
- Publication date
- 29 January 2026
- Language
- EN