2024/01/23 by Vilma Orgoványi, Orgoványi, Vilma, Károly Simon +1
Mathematics · #60J80 #60J85 (Primary) 28A80 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2401.12767
openalex publication_date 2024/01/23 · openalex created_date 2024/01/25 · openalex updated_date 2026/07/31
It is well known that under some conditions the almost sure survival probability of a multitype branching processes 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 in the line.