scholarly journals Application of the interacting particle system method to piecewise deterministic Markov processes used in reliability

2019 ◽  
Vol 29 (6) ◽  
pp. 063119 ◽  
Author(s):  
Hassane Chraibi ◽  
Anne Dutfoy ◽  
Thomas Galtier ◽  
Josselin Garnier
Keyword(s):  
Markov Processes ◽  
Particle System ◽  
Interacting Particle System ◽  
Interacting Particle ◽  
System Method ◽  
Piecewise Deterministic Markov Processes

scholarly journals A Local Barycentric Version of the Bak–Sneppen Model

2021 ◽  
Vol 182 (2) ◽  
Author(s):  
Philip Kennerberg ◽  
Stanislav Volkov
Keyword(s):  
Real Number ◽  
Uniform Distribution ◽  
Particle System ◽  
Interacting Particle System ◽  
Interacting Particle

AbstractWe study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let $$N\ge 3$$ N ≥ 3 vertices be placed on a circle, such that each vertex has exactly two neighbours. To each vertex assign a real number, called fitness (we use this term, as it is quite standard for Bak–Sneppen models). Now find the vertex which fitness deviates most from the average of the fitnesses of its two immediate neighbours (in case of a tie, draw uniformly among such vertices), and replace it by a random value drawn independently according to some distribution $$\zeta $$ ζ . We show that in case where $$\zeta $$ ζ is a finitely supported or continuous uniform distribution, all the fitnesses except one converge to the same value.

scholarly journals Hydrodynamic limit for a nongradient interacting particle system with stochastic reservoirs

2000 ◽  
Vol 45 (4) ◽  
pp. 694-717 ◽  
Author(s):  
Claudio Landim ◽  
Claudio Landim ◽  
Claudio Landim ◽  
Claudio Landim ◽  
Mustapha Mourragui ◽  
...  
Keyword(s):  
Hydrodynamic Limit ◽  
Particle System ◽  
Interacting Particle System ◽  
Interacting Particle

Segregation in an interacting particle system

2000 ◽  
Vol 271 (1-2) ◽  
pp. 92-99 ◽  
Author(s):  
Kei-ichi Tainaka ◽  
Nariyuki Nakagiri
Keyword(s):  
Particle System ◽  
Interacting Particle System ◽  
Interacting Particle

scholarly journals A multitype contact process with frozen sites: a spatial model of allelopathy

2005 ◽  
Vol 42 (04) ◽  
pp. 1109-1119
Author(s):  
Nicolas Lanchier
Keyword(s):  
Phase Transitions ◽  
Spatial Model ◽  
Biological Process ◽  
Particle System ◽  
Contact Process ◽  
Interacting Particle System ◽  
Interacting Particle

In this paper, we introduce a generalization of the two-color multitype contact process intended to mimic a biological process called allelopathy. To be precise, we have two types of particle. Particles of each type give birth to particles of the same type, and die at rate 1. When a particle of type 1 dies, it gives way to a frozen site that blocks particles of type 2 for an exponentially distributed amount of time. Specifically, we investigate in detail the phase transitions and the duality properties of the interacting particle system.

The annihilating process on random trees and the square lattice

2004 ◽  
Vol 41 (3) ◽  
pp. 816-831
Author(s):  
Aidan Sudbury
Keyword(s):  
Survival Probability ◽  
Particle System ◽  
Random Trees ◽  
Interacting Particle System ◽  
Random Tree ◽  
Square Lattice ◽  
One Dimensional ◽  
Interacting Particle

An annihilating process is an interacting particle system in which the only interaction is that a particle may kill a neighbouring particle. Since there is no birth and no movement, once a particle has no neighbours its site remains occupied for ever. The survival probability is calculated for a random tree and for the square lattice. A connection is made between annihilating processes and the adsorption of molecules onto surfaces. A one-dimensional adsorption problem is solved in the case in which the two neighbours do not act independently.

Interacting particle systems approximations of the Kushner-Stratonovitch equation

1999 ◽  
Vol 31 (3) ◽  
pp. 819-838 ◽  
Author(s):  
D. Crişan ◽  
P. Del Moral ◽  
T. J. Lyons
Keyword(s):  
Continuous Time ◽  
Order Of Convergence ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Particle Systems ◽  
Interacting Particle System ◽  
Order Convergence ◽  
Interacting Particle ◽  
Convergence Results ◽  
Filtering Problem

In this paper we consider the continuous-time filtering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works. We will discuss how the discrete time approximating model of the Kushner-Stratonovitch equation and the genetic type interacting particle system approximation combine. We present quenched error bounds as well as mean order convergence results.

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