Complete left-tail asymptotic for branching processes with immigration
Abstract
Abstract We derive a complete left-tail asymptotic series for the density of the martingale limit of a Galton–Watson process with immigration. We show that the series converges everywhere, not only for small arguments. This is the first complete result regarding the left tails of branching processes with immigration. A good, quickly computed approximation for the density will also be derived from the series.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Random Matrices and Applications
Stochastic processes and financial applications
Publication details
- Journal / source
- Journal of Applied Probability
- Pages
- 1–13
- Publication date
- 10 August 2026
- Language
- EN