6 papers
Left-tail expansions for Schröder branching processes with explicit convergence rates
Anton A. Kutsenko
In previous work, the density of the martingale limit in Schröder branching processes was expressed as a convergent double power-law series with oscillatory terms. The proof relied…
On some explicit integrals related to "fractal foothills"
Anton A Kutsenko
In the previous papers, we tried to analyze the complete loop counting functions that count all the loops in an infinite random walk represented by digits of a real number. In this…
Complete left tail asymptotic for supercritical multitype branching processes
Anton A. Kutsenko
We derive a complete left-tail asymptotic series for the density of the {\it martingale limit} of a supercritical multitype Galton-Watson process in the Schröder case. We show tha…
Complete left tail asymptotic for branching processes in random environments
Anton A Kutsenko
Recently, the complete left tail asymptotic for the density of the {\it martingale limit} of the classical Galton-Watson process has been derived. The derivation is based on the pr…
Complete left-tail asymptotic for branching processes with immigration
Anton A Kutsenko
We derive a complete left-tail asymptotic series for the density of the {\it martingale limit} of a Galton-Watson process with immigration. We show that the series converges everyw…
Complete right tail asymptotic for the density of branching processes with fractional generating functions
Anton A. Kutsenko
The right tail asymptotic series consisting of attenuating exponential terms are derived for the densities of Galton-Watson processes with fractional probability generating functio…