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

1998 ◽  
pp. 163-180 ◽  
Author(s):  
James Pitman
Keyword(s):  
Random Walks ◽  
Branching Processes

scholarly journals Harry Kesten’s work in probability theory

2021 ◽  
Author(s):  
Geoffrey R. Grimmett
Keyword(s):  
Probability Theory ◽  
Random Walks ◽  
Branching Processes

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.

RANDOM WALKS WITH HEAVY TAILS AND LIMIT THEOREMS FOR BRANCHING PROCESSES WITH MIGRATION AND IMMIGRATION

2012 ◽  
Vol 12 (01) ◽  
pp. 1150007 ◽  
Author(s):  
YAQIN FENG ◽  
STANISLAV MOLCHANOV ◽  
JOSEPH WHITMEYER
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Heavy Tails ◽  
Stochastic Dynamics ◽  
Branching Processes ◽  
Spatial Dynamics ◽  
Limiting Distributions ◽  
Central Result

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.

scholarly journals Measure-valued branching processes associated with random walks on $p$-adics

2000 ◽  
Vol 28 (4) ◽  
pp. 1680-1710 ◽  
Author(s):  
Sergio Albeverio ◽  
Xuelei Zhao
Keyword(s):  
Random Walks ◽  
Branching Processes

scholarly journals Recurrence and Transience of Critical Branching Processes in Random Environment with Immigration and an Application to Excited Random Walks

2014 ◽  
Vol 46 (03) ◽  
pp. 687-703 ◽  
Author(s):  
Elisabeth Bauernschubert
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Environment ◽  
Branching Processes ◽  
Random Environments ◽  
Recurrent Random Walk ◽  
The Right

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.

scholarly journals An Almost-Sure Renewal Theorem for Branching Random Walks on the Line

2010 ◽  
Vol 47 (03) ◽  
pp. 811-825
Author(s):  
Matthias Meiners
Keyword(s):  
Random Walks ◽  
Real Line ◽  
Branching Processes ◽  
Almost Sure Convergence ◽  
General Characteristic ◽  
Renewal Theorem ◽  
The Real ◽  
Branching Random Walks

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.

scholarly journals Random Walks and Branching Processes in Correlated Gaussian Environment

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

scholarly journals Asymptotics of Posteriors for Binary Branching Processes

2008 ◽  
Vol 45 (03) ◽  
pp. 727-742
Author(s):  
Didier Piau
Keyword(s):  
Random Walks ◽  
Central Limit ◽  
Limit Theorems ◽  
Branching Processes ◽  
Central Limit Theorems ◽  
Hitting Times ◽  
Initial Population ◽  
Posterior Distributions ◽  
Bayesian Procedure

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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