Evolution of Complex Systems and 1f Noise: From Physics to Financial Markets

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Evolution of Complex Systems and 1/f Noise From
Physics to Financial Markets
V. Gontis, B. Kaulakys, M. Alaburda and J.
Ruseckas, Institute of Theoretical Physics and
Astronomy, Vilnius University, gontis_at_ktl.mii.lt
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Evolution of the complexity into chaotic regime

• Complex systems with the elements of
  self-organization DNA base sequence structure,
  cellular automata, complex networks and traffic
  flow, economics, financial markets
• 1/f noise - characteristic signature of
  complexity exhibiting self organized criticality
• Is it possible to define a stochastic model
  system exhibiting fractal statistics, criticality
  and 1/f noise ?

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Fractal (power-law) stochastic processes
Physics resistors, semiconductors, vacuum
tubes, photon-counting .. Biomedicine
neurotransmitters, heartbeat dynamics, Social
systems financial markets, traffics, network
models .. Geophysics earthquakes . Elsewhere
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Point process as a model of 1/f noise
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Stochastic models of interevent time

• Poisson processes
• Fractal renewal processes

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Recurrent stochastic point processes
B. Kaulakys and T. Meskauskas, Phys. Rev. E 58
(1998) 7013-7019
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Power spectral density
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Counting statistics
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Conclusions

• We introduced the multiplicative stochastic point
  process as a model of power-law noise
• The model exhibits power law behavior in several
  statistics and serves as a generic model of 1/f
  noise
• We do suggest this model as a stochastic limit
  of self organized criticality in complex systems