scholarly journals Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion

2005 ◽  
Vol 33 (1) ◽  
pp. 194-222 ◽  
Author(s):  
Jean-François Le Gall ◽  
Leonid Mytnik
Keyword(s):  
Brownian Motion ◽  
Integral Representation ◽  
Stochastic Integral ◽  
Stochastic Integral Representation ◽  
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

INTEGRAL REPRESENTATION OF QUANTUM MARTINGALES

2005 ◽  
Vol 08 (01) ◽  
pp. 55-72 ◽  
Author(s):  
UN CIG JI ◽  
KALYAN B. SINHA
Keyword(s):  
Integral Representation ◽  
Wide Class ◽  
Stochastic Integral ◽  
Integral Kernel ◽  
Integral Operators ◽  
Second Quantization ◽  
Kernel Operator ◽  
Stochastic Integral Representation ◽  
Singular Kernels

A stochastic integral representation in terms of generalized integral kernel operator is proved for a wide class of quantum martingales which includes regular martingales and the martingales determined by the second quantization of integral operators containing singular kernels.

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.

Quasi-free stochastic integral representation theorems over the CCR

1988 ◽  
Vol 104 (2) ◽  
pp. 383-398 ◽  
Author(s):  
Ivan F. Wilde
Keyword(s):  
Hilbert Space ◽  
Integral Representation ◽  
Stochastic Integral ◽  
Stochastic Integrals ◽  
Representation Theorems ◽  
Martingale Representation ◽  
Stochastic Integral Representation ◽  
Vector Valued ◽  
General Vector

AbstractIt is shown that each vector in the Hilbert space of certain quasi-free representations of the CCR can be written uniquely in terms of quantum stochastic integrals. As a consequence, we obtain general vector-valued and operator-valued boson quantum martingale representation theorems.

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