scholarly journals Moment Densities of Super Brownian Motion, and a Harnack Estimate for a Class of X-harmonic Functions

2014 ◽  
Vol 41 (4) ◽  
pp. 1347-1358
Author(s):  
Thomas S. Salisbury ◽  
A. Deniz Sezer
Keyword(s):  
Brownian Motion ◽  
Harmonic Functions ◽  
Harnack Estimate ◽  
Super Brownian Motion

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.

scholarly journals Kolmogorov's test for super-Brownian motion

1998 ◽  
Vol 26 (3) ◽  
pp. 1041-1056 ◽  
Author(s):  
Jean-Stéphane Dhersin ◽  
Jean-François Le Gall
Keyword(s):  
Brownian Motion ◽  
Super Brownian Motion

scholarly journals Brownian Motion and Harmonic Analysis on Sierpinski Carpets

1999 ◽  
Vol 51 (4) ◽  
pp. 673-744 ◽  
Author(s):  
Martin T. Barlow ◽  
Richard F. Bass
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Heat Kernel ◽  
Lower Bounds ◽  
Harnack Inequality ◽  
Harmonic Functions ◽  
Upper And Lower Bounds ◽  
Isotropic Diffusion ◽  
Sierpinski Carpets

AbstractWe consider a class of fractal subsets of d formed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusion X and determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.

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