Enumerations of trees and forests related to branching processes and random walks

Author(s):  
James Pitman
Author(s):  
Geoffrey R. Grimmett

AbstractWe survey the published work of Harry Kesten in probability theory, with emphasis on his contributions to random walks, branching processes, percolation, and related topics.


2012 ◽  
Vol 12 (01) ◽  
pp. 1150007 ◽  
Author(s):  
YAQIN FENG ◽  
STANISLAV MOLCHANOV ◽  
JOSEPH WHITMEYER

The central result of this paper is the existence of limiting distributions for two classes of critical homogeneous-in-space branching processes with heavy tails spatial dynamics in dimension d = 2. In dimension d ≥ 3, the same results are true without any special assumptions on the underlying (non-degenerated) stochastic dynamics.


2000 ◽  
Vol 28 (4) ◽  
pp. 1680-1710 ◽  
Author(s):  
Sergio Albeverio ◽  
Xuelei Zhao

2014 ◽  
Vol 46 (03) ◽  
pp. 687-703 ◽  
Author(s):  
Elisabeth Bauernschubert

We establish recurrence and transience criteria for critical branching processes in random environments with immigration. These results are then applied to the recurrence and transience of a recurrent random walk in a random environment on ℤ disturbed by cookies inducing a drift to the right of strength 1.


2010 ◽  
Vol 47 (03) ◽  
pp. 811-825
Author(s):  
Matthias Meiners

In the present paper an almost-sure renewal theorem for branching random walks (BRWs) on the real line is formulated and established. The theorem constitutes a generalization of Nerman's theorem on the almost-sure convergence of Malthus normed supercritical Crump-Mode-Jagers branching processes counted with general characteristic and Gatouras' almost-sure renewal theorem for BRWs on a lattice.


2016 ◽  
Vol 166 (1) ◽  
pp. 1-23
Author(s):  
Frank Aurzada ◽  
Alexis Devulder ◽  
Nadine Guillotin-Plantard ◽  
Françoise Pène

2008 ◽  
Vol 45 (03) ◽  
pp. 727-742
Author(s):  
Didier Piau

We compute the posterior distributions of the initial population and parameter of binary branching processes in the limit of a large number of generations. We compare this Bayesian procedure with a more naïve one, based on hitting times of some random walks. In both cases, central limit theorems are available, with explicit variances.


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