scholarly journals Limiting Distribution of Particles Near the Frontier in the Catalytic Branching Brownian Motion

2020 ◽  
Vol 169 (1) ◽  
pp. 433-453
Author(s):  
Sergey Bocharov
2019 ◽  
Vol 56 (3) ◽  
pp. 891-917
Author(s):  
Sergey Bocharov ◽  
Li Wang

AbstractWe consider a model of branching Brownian motion in which the usual spatially homogeneous branching and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain time-dependent regions and as a consequence the first-order asymptotic behaviour of the rightmost particle.


2015 ◽  
Vol 51 (4) ◽  
pp. 1215-1250 ◽  
Author(s):  
Julien Berestycki ◽  
Nathanaël Berestycki ◽  
Jason Schweinsberg

2012 ◽  
Vol 49 (03) ◽  
pp. 671-684
Author(s):  
A. E. Kyprianou ◽  
A. Murillo-Salas ◽  
J. L. Pérez

We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki, Kyprianou and Murillo-Salas (2011). In particular, by considering existing results for branching Brownian motion due to Harris and Kyprianou (2006) and Maillard (2011), we obtain, with relative ease, conclusions regarding the growth in the right-most point in the support, analytical properties of the associated one-sided Fisher-Kolmogorov-Petrovskii-Piscounov wave equation, as well as the distribution of mass on the exit measure associated with the barrier.


1997 ◽  
Vol 108 (2) ◽  
pp. 171-192 ◽  
Author(s):  
Steven P. Lalley ◽  
Tom Sellke

2013 ◽  
Vol 10 (2) ◽  
pp. 1205-1251
Author(s):  
Louigi Addario-Berry ◽  
Nathanaël Berestycki ◽  
Nina Gantert

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