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).

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Virginie Collette

Last modified: Mon Aug 4 16:24:15 CEST 2008