scholarly journals On the jump-diffusion approximation of stochastic difference equations driven by a mixing sequence

1990 ◽  
Vol 42 (3) ◽  
pp. 353-376 ◽  
Author(s):  
Tsukasa FUJIWARA
Keyword(s):  
Difference Equations ◽  
Diffusion Approximation ◽  
Jump Diffusion ◽  
Stochastic Difference Equations ◽  
Mixing Sequence

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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