Two-Dimensional Limit Theorem for a Critical Catalytic Branching Random Walk

2004 ◽  
pp. 387-395 ◽  
Author(s):  
Valentin Topchii ◽  
Vladimir Vatutin
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Branching Random Walk ◽  
Two Dimensional ◽  
Catalytic Branching

scholarly journals Individuals at the origin in the critical catalytic branching random walk

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Valentin Topchii ◽  
Vladimir Vatutin
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Continuous Time ◽  
Branching Random Walk ◽  
Conditional Limit Theorem ◽  
Catalytic Branching ◽  
International Audience ◽  
Number Of Individuals ◽  
Conditional Limit

International audience A continuous time branching random walk on the lattice $\mathbb{Z}$ is considered in which individuals may produce children at the origin only. Assuming that the underlying random walk is symmetric and the offspring reproduction law is critical we prove a conditional limit theorem for the number of individuals at the origin.

Maximum of a catalytic branching random walk

2019 ◽  
Vol 74 (3) ◽  
pp. 546-548 ◽  
Author(s):  
E. Vl. Bulinskaya
Keyword(s):  
Random Walk ◽  
Branching Random Walk ◽  
Catalytic Branching
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