scholarly journals Branching and interacting particle systems approximations of feynman-kac formulae with applications to non-linear filtering

2000 ◽  
pp. 1-145 ◽  
Author(s):  
P. Del Moral ◽  
L. Miclo
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Linear Filtering ◽  
Interacting Particle ◽  
Non Linear

scholarly journals Condensation of SIP Particles and Sticky Brownian Motion

2021 ◽  
Vol 183 (3) ◽  
Author(s):  
Mario Ayala ◽  
Gioia Carinci ◽  
Frank Redig
Keyword(s):  
Brownian Motion ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Self Duality ◽  
Inclusion Process ◽  
Interacting Particle ◽  
New Information ◽  
Homogeneous Product ◽  
Coarsening Dynamics ◽  
The Difference

AbstractWe study the symmetric inclusion process (SIP) in the condensation regime. We obtain an explicit scaling for the variance of the density field in this regime, when initially started from a homogeneous product measure. This provides relevant new information on the coarsening dynamics of condensing interacting particle systems on the infinite lattice. We obtain our result by proving convergence to sticky Brownian motion for the difference of positions of two SIP particles in the sense of Mosco convergence of Dirichlet forms. Our approach implies the convergence of the probabilities of two SIP particles to be together at time t. This, combined with self-duality, allows us to obtain the explicit scaling for the variance of the fluctuation field.

scholarly journals Holomorphic Bogoliubov functionals for interacting particle systems in continuum

2006 ◽  
Vol 238 (2) ◽  
pp. 375-404 ◽  
Author(s):  
Yuri G. Kondratiev ◽  
Tobias Kuna ◽  
Maria João Oliveira
Keyword(s):  
Interacting Particle Systems ◽  
Particle Systems ◽  
Interacting Particle
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