scholarly journals An exit measure construction of the total local time of super-Brownian motion

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Jieliang Hong
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Super Brownian Motion ◽  
Exit Measure

scholarly journals An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier

2012 ◽  
Vol 49 (03) ◽  
pp. 671-684
Author(s):  
A. E. Kyprianou ◽  
A. Murillo-Salas ◽  
J. L. Pérez
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Relative Ease ◽  
Branching Brownian Motion ◽  
Analytical Properties ◽  
Super Brownian Motion ◽  
Exit Measure ◽  
The Right

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.

Some properties of the exit measure for super Brownian motion

2002 ◽  
Vol 122 (1) ◽  
pp. 71-107
Author(s):  
Romain Abraham ◽  
Jean-François Delmas
Keyword(s):  
Brownian Motion ◽  
Super Brownian Motion ◽  
Exit Measure

scholarly journals An Application of the Backbone Decomposition to Supercritical Super-Brownian Motion with a Barrier

2012 ◽  
Vol 49 (3) ◽  
pp. 671-684 ◽  
Author(s):  
A. E. Kyprianou ◽  
A. Murillo-Salas ◽  
J. L. Pérez
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Relative Ease ◽  
Branching Brownian Motion ◽  
Analytical Properties ◽  
Super Brownian Motion ◽  
Exit Measure ◽  
The Right

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.

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