Power fractional laws in branching models
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Gerold Alsmeyer from Uni Münster
| Abstract: | Power fractional laws, first introduced by Sagitov and Lindo [6], form a generalization
of linear fractional laws. The latter have their well-established place in the theory of
branching processes because, when used to model reproduction, often lead to more explicit
results than other distributions on the set of integers. This is even true in the situation
of an underlying random environment as recently demonstrated in the expository article
[1]. After an introduction of some fundamental properties of power fractional laws, this
talk aims to explain that they form a useful extension for which explicit results can still be
obtained to an extent far beyond the general case. This will be exemplified by some typical
examples in both fixed and i.i.d. random environment, the latter leading to a connection
with affine linear recursions and perpetuities as in the linear fractional case. If time allows,
I will also talk about recent work with Hu and Mallein [3] on the Derrida-Retaux model in
the linear-fractional case. The first part of the talk is based on joint work with Viet Hung
Hoang [2].
Acknowledgements: Work partially funded by the Deutsche Forschungsgemeinschaft
(DFG) under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Münster:
Dynamics–Geometry–Structure. |