Approximation to the Finite Sample Distribution for Nonstable First Order Stochastic Difference Equations

Econometrica ◽  
1984 ◽  
Vol 52 (5) ◽  
pp. 1271 ◽  
Author(s):  
S. E. Satchell
Keyword(s):  
Difference Equations ◽  
Finite Sample ◽  
Sample Distribution ◽  
Stochastic Difference Equations ◽  
First Order ◽  
Finite Sample Distribution

scholarly journals Examination of Particle Tails

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
Tim Blackwell ◽  
Dan Bratton
Keyword(s):  
Power Law ◽  
Difference Equations ◽  
Particle Swarm ◽  
Second Order ◽  
Particle Swarm Optimisation ◽  
Position Distribution ◽  
Length Scales ◽  
Stochastic Difference Equations ◽  
First Order ◽  
Second Order Equations

The tail of the particle swarm optimisation (PSO) position distribution at stagnation is shown to be describable by a power law. This tail fattening is attributed to particle bursting on all length scales. The origin of the power law is concluded to lie in multiplicative randomness, previously encountered in the study of first-order stochastic difference equations, and generalised here to second-order equations. It is argued that recombinant PSO, a competitive PSO variant without multiplicative randomness, does not experience tail fattening at stagnation.

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