On a variational problem for an infinite particle system in a random medium Part II: The local growth rate

1994 ◽  
Vol 100 (3) ◽  
pp. 301-328 ◽  
Author(s):  
A. Greven ◽  
F. den Hollander
Keyword(s):  
Growth Rate ◽  
Variational Problem ◽  
Particle System ◽  
Random Medium ◽  
Local Growth ◽  
Infinite Particle System ◽  
Infinite Particle

An infinite particle system with continual input and random death

1978 ◽  
Vol 10 (04) ◽  
pp. 764-787
Author(s):  
J. N. McDonald ◽  
N. A. Weiss
Keyword(s):  
Markov Chain ◽  
State Space ◽  
Limit Theorems ◽  
Particle System ◽  
Countable State Space ◽  
Infinite Particle System ◽  
Large Numbers ◽  
Countable State ◽  
Infinite Particle ◽  
Number Of Particles

At times n = 0, 1, 2, · · · a Poisson number of particles enter each state of a countable state space. The particles then move independently according to the transition law of a Markov chain, until their death which occurs at a random time. Several limit theorems are then proved for various functionals of this infinite particle system. In particular, laws of large numbers and central limit theorems are proved.

Functionals of an infinite particle system with independent motions, creation, and annihilation

1974 ◽  
Vol 6 (4) ◽  
pp. 636-650 ◽  
Author(s):  
P. A. Jacobs
Keyword(s):  
State Space ◽  
Central Limit ◽  
Limit Theorems ◽  
Particle System ◽  
Central Limit Theorems ◽  
The Other ◽  
Strong Laws ◽  
Infinite Particle System ◽  
Infinite Particle ◽  
Random Times

Particles enter a state space at random times. Each particle travels in the space independent of the other particles until its death. Functionals of the particle system are studied with strong laws and central limit theorems being obtained.

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