Limit distributions for minimal displacement of branching random walks

1991 ◽  
Vol 90 (3) ◽  
pp. 403-426 ◽  
Author(s):  
F. M. Dekking ◽  
B. Host
Keyword(s):  
Random Walks ◽  
Limit Distributions ◽  
Branching Random Walks

Limit distributions for the number of particles in branching random walks

2011 ◽  
Vol 90 (5-6) ◽  
pp. 824-837
Author(s):  
E. Vl. Bulinskaya
Keyword(s):  
Random Walks ◽  
Limit Distributions ◽  
Branching Random Walks ◽  
Number Of Particles

Limit distributions arising in branching random walks on integer lattices

2011 ◽  
Vol 51 (3) ◽  
pp. 310-321 ◽  
Author(s):  
Ekaterina Vl. Bulinskaya
Keyword(s):  
Random Walks ◽  
Limit Distributions ◽  
Branching Random Walks ◽  
Integer Lattices

scholarly journals Strong Local Survival of Branching Random Walks is Not Monotone

2014 ◽  
Vol 46 (02) ◽  
pp. 400-421 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Generating Function ◽  
Continuous Time ◽  
Local Property ◽  
Branching Random Walk ◽  
Infinite Dimensional ◽  
Branching Random Walks ◽  
Local Survival ◽  
Branching Law

In this paper we study the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite-dimensional generating functionGand a maximum principle which, we prove, is satisfied by every fixed point ofG. We give results for the existence of a strong local survival regime and we prove that, unlike local and global survival, in continuous time, strong local survival is not a monotone property in the general case (though it is monotone if the branching random walk is quasitransitive). We provide an example of an irreducible branching random walk where the strong local property depends on the starting site of the process. By means of other counterexamples, we show that the existence of a pure global phase is not equivalent to nonamenability of the process, and that even an irreducible branching random walk with the same branching law at each site may exhibit nonstrong local survival. Finally, we show that the generating function of an irreducible branching random walk can have more than two fixed points; this disproves a previously known result.

scholarly journals Strong Local Survival of Branching Random Walks is Not Monotone

2014 ◽  
Vol 46 (2) ◽  
pp. 400-421 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Generating Function ◽  
Continuous Time ◽  
Local Property ◽  
Branching Random Walk ◽  
Infinite Dimensional ◽  
Branching Random Walks ◽  
Local Survival ◽  
Branching Law

In this paper we study the strong local survival property for discrete-time and continuous-time branching random walks. We study this property by means of an infinite-dimensional generating function G and a maximum principle which, we prove, is satisfied by every fixed point of G. We give results for the existence of a strong local survival regime and we prove that, unlike local and global survival, in continuous time, strong local survival is not a monotone property in the general case (though it is monotone if the branching random walk is quasitransitive). We provide an example of an irreducible branching random walk where the strong local property depends on the starting site of the process. By means of other counterexamples, we show that the existence of a pure global phase is not equivalent to nonamenability of the process, and that even an irreducible branching random walk with the same branching law at each site may exhibit nonstrong local survival. Finally, we show that the generating function of an irreducible branching random walk can have more than two fixed points; this disproves a previously known result.

Branching Random Walks with Heavy Tails

2013 ◽  
Vol 42 (16) ◽  
pp. 3001-3010 ◽  
Author(s):  
Elena Yarovaya
Keyword(s):  
Random Walks ◽  
Heavy Tails ◽  
Branching Random Walks

scholarly journals Area of Brownian Motion with Generatingfunctionology

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Michel Nguyên Thê
Keyword(s):  
Brownian Motion ◽  
Random Walks ◽  
Generating Functions ◽  
Limit Distributions ◽  
Dyck Paths ◽  
Different Types ◽  
International Audience

International audience This paper gives a survey of the limit distributions of the areas of different types of random walks, namely Dyck paths, bilateral Dyck paths, meanders, and Bernoulli random walks, using the technology of generating functions only.

scholarly journals Global survival of branching random walks and tree-like branching random walks

2017 ◽  
Vol 14 (1) ◽  
pp. 381
Author(s):  
Daniela Bertacchi ◽  
Cristian F. Coletti ◽  
Fabio Zucca
Keyword(s):  
Random Walks ◽  
Branching Random Walks ◽  
Global Survival

Branching Random Walks and Martingales

2015 ◽  
pp. 19-28 ◽  
Author(s):  
Zhan Shi
Keyword(s):  
Random Walks ◽  
Branching Random Walks

Branching Random Walks

2015 ◽  
Author(s):  
Zhan Shi
Keyword(s):  
Random Walks ◽  
Branching Random Walks
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