Séminaire du 8 septembre 2008. 14h00: On a Certain Functional Equation: Oscillations in the solutions and their Taylor Coefficients. Stefan Gerhold,
Vienna University of Technology, Austria.
The equilibrium distribution of branching processes with immigration is governed by a functional equation. Explicitly, its solutions can be written as infinite products of iterated functions. We determine their asymptotic behavior, using Poincare-Schroeder functional equations, complex dynamics, and Mellin transform asymptotics. The oscillations in the Taylor coefficients are revealed by a variant of Flajolet and Odlyzko's singularity analysis technique. This work, done in collaboration with Michael Drmota, complements and extends results by de Bruijn (Nederl. Akad. Wetensch. Indag. Math. 1979).
Last modified: Mon Aug 4 16:24:15 CEST 2008