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Generalized Schröder-type functional equations for Galton-Watson processes in random environments
Anton A. Kutsenko
The classical Galton--Watson process works with a fixed probability of fission at each time step. One of the generalizations is that the probabilities depend on time. We consider o…
A formula for the periodic multiplier in left tail asymptotics for supercritical branching processes in the Schröder case
Anton A. Kutsenko
It is known that the left tail asymptotic for supercritical branching processes in the Schröder case satisfies a power law multiplied by some multiplicatively periodic function. We…
Complete left tail asymptotic for the density of branching processes in the Schröder case
Anton A. Kutsenko
For the density of Galton-Watson processes in the Schröder case, we derive a complete left tail asymptotic series consisting of power terms multiplied by periodic factors.
Periodic oscillations of coefficients of power series that satisfy functional equations, a practical revision
Anton A Kutsenko
For the solutions of functional equations , we derive a complete asymptotic of power series coefficients. As an application, we improve significantly an a…