Convex solutions of a Schröder equation in several variables

Author:

Hoppe Fred M.

Abstract

A nonprobabilistic proof is given for the existence of the Yaglom conditional limit distribution for the subcritical multitype Galton-Watson process by using a uniqueness theorem for convex solutions of the multidimensional Schröder functional equation.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

1. Slowly varying functions and asymptotic relations;Bojanić, R.;J. Math. Anal. Appl.,1971

2. A refinement of two theorems in the theory of branching processes;Heathcote, C. R.;Teor. Verojatnost. i Primenen.,1967

3. Stationary measures for multitype branching processes;Hoppe, Fred;J. Appl. Probability,1975

4. \bysame(1975b), Functional equations with applications to multitype Gallon-Watson branching processes, Doctoral Dissertation, Princeton Univ., Princeton, N.J.

5. Representations of invariant measures on multitype Galton-Watson processes;Hoppe, Fred M.;Ann. Probability,1977

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