• Limit Theorems for Exceedances of Sequence of Branching Processes
Ibrahim Rahimov and Husna Hasan
Abstract. A problem of the first exceedance of a given level by the family of independent branching processes with and without immigration is considered. Using limit theorems for large deviations for processes with and without immigration limit theorems for the index of the first process exceeding some fixed or increasing levels in critical, subcritical and supercritical cases are proved. Asymptotic formulas for the expectation of the index are also obtained.