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Computer simulation of attractors in stochastic models with α-stable noise


  • Janicki, Aleksander
  • Weron, Aleksander


The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to 2nd order stochastic differential equations, subject to large random external disturbances with infinite variance, described by α-stable Lévy motion processes. This provides us with qualitative and quantitative information on their asymptotic behavior, and, in particular, with graphical visualization of stochastic attractors in appropriate phase spaces.

Suggested Citation

  • Janicki, Aleksander & Weron, Aleksander, 1995. "Computer simulation of attractors in stochastic models with α-stable noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 9-19.
  • Handle: RePEc:eee:matcom:v:39:y:1995:i:1:p:9-19
    DOI: 10.1016/0378-4754(95)00132-H

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    References listed on IDEAS

    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
    2. Aleksander Janicki & Aleksander Weron, 1994. "Can One See Alpha-stable Variables and Processes?," HSC Research Reports HSC/94/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    3. West, Bruce J. & Seshadri, V., 1982. "Linear systems with Lévy fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 203-216.
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    1. Janusz Gajda & Aleksandra Grzesiek & Agnieszka Wyłomańska, 2023. "Ornstein - Uhlenbeck Process Driven By $$\alpha$$ α -stable Process and Its Gamma Subordination," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.

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