Asymptotic behaviour of stochastic systems with conditionally exponential decay property

Agnieszka Jurlewicz; Aleksander Weron; Karina Weron

Applicationes Mathematicae (1996)

  • Volume: 23, Issue: 4, page 379-394
  • ISSN: 1233-7234

Abstract

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A new class of CED systems, providing insight into behaviour of physical disordered materials, is introduced. It includes systems in which the conditionally exponential decay property can be attached to each entity. A limit theorem for the normalized minimum of a CED system is proved. Employing different stable schemes the universal characteristics of the behaviour of such systems are derived.

How to cite

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Jurlewicz, Agnieszka, Weron, Aleksander, and Weron, Karina. "Asymptotic behaviour of stochastic systems with conditionally exponential decay property." Applicationes Mathematicae 23.4 (1996): 379-394. <http://eudml.org/doc/219140>.

@article{Jurlewicz1996,
abstract = {A new class of CED systems, providing insight into behaviour of physical disordered materials, is introduced. It includes systems in which the conditionally exponential decay property can be attached to each entity. A limit theorem for the normalized minimum of a CED system is proved. Employing different stable schemes the universal characteristics of the behaviour of such systems are derived.},
author = {Jurlewicz, Agnieszka, Weron, Aleksander, Weron, Karina},
journal = {Applicationes Mathematicae},
keywords = {stable distributions; minima of random sequences; stochastic CED systems; reaction kinetics; dielectric relaxation; stability of stochastic models},
language = {eng},
number = {4},
pages = {379-394},
title = {Asymptotic behaviour of stochastic systems with conditionally exponential decay property},
url = {http://eudml.org/doc/219140},
volume = {23},
year = {1996},
}

TY - JOUR
AU - Jurlewicz, Agnieszka
AU - Weron, Aleksander
AU - Weron, Karina
TI - Asymptotic behaviour of stochastic systems with conditionally exponential decay property
JO - Applicationes Mathematicae
PY - 1996
VL - 23
IS - 4
SP - 379
EP - 394
AB - A new class of CED systems, providing insight into behaviour of physical disordered materials, is introduced. It includes systems in which the conditionally exponential decay property can be attached to each entity. A limit theorem for the normalized minimum of a CED system is proved. Employing different stable schemes the universal characteristics of the behaviour of such systems are derived.
LA - eng
KW - stable distributions; minima of random sequences; stochastic CED systems; reaction kinetics; dielectric relaxation; stability of stochastic models
UR - http://eudml.org/doc/219140
ER -

References

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  1. P. Billingsley (1979), Probability and Measure, Wiley, New York. Zbl0411.60001
  2. L. Breiman (1992), Probability, SIAM, Philadelphia. 
  3. L. A. Dissado and R. M. Hill (1987), Self-similarity as a fundamental feature of the regression of fluctuations, Chem. Phys. 111, 193-207. 
  4. W. Feller (1966), An Introduction to Probability and Its Applications, Vol. 2, Wiley, New York. Zbl0138.10207
  5. M. R. de la Fuente, M. A. Perez Jubindo and M. J. Tello (1988), Two-level model for the nonexponential Williams-Watts dielectric relaxation, Phys. Rev. B37, 2094-2101. 
  6. A. Hunt (1994), On the 'universal' scaling of the dielectric relaxation in dipole liquids and glasses, J. Phys.: Condens. Matter, to appear. 
  7. A. Janicki and A. Weron (1994), Can one see α-stable variables and processes? Statist. Sci. 9, 109-126. Zbl0955.60508
  8. A. K. Jonscher (1983), Dielectric Relaxation in Solids, Chelsea Dielectrics, London. 
  9. J. Klafter and M. F. Shlesinger (1986), On the relationship among three theorems of relaxation in disordered systems, Proc. Nat. Acad. Sci. U.S.A. 83, 848-851. 
  10. J. Klafter, M. F. Shlesinger, G. Zumoffen and A. Blumen (1992), Scale invariance in anomalous diffusion, Phil. Mag. B65, 755-765. 
  11. M. R. Leadbetter, G. Lindgren and H. Rootzen (1986), Extremes and Related Properties of Random Sequences and Processes, Springer, New York. Zbl0518.60021
  12. S. Mittnik and S. T. Rachev (1991), Modelling asset returns with alternative stable distributions, Stony Brook Working Papers WP-91-05 1-63. 
  13. E. W. Montroll and J. T. Bendler (1984), 
  14. On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation, J. Statist. Phys. 34, 129-162. Zbl0598.60100
  15. R. G. Palmer, D. L. Stein, E. Abrahams and P. W. Anderson (1984), Models of hierarchically constrained dynamics for glassy relaxation, Phys. Rev. Lett. 53, 958-961. 
  16. A. Płonka (1991), Developments in dispersive kinetics, Prog. Reaction Kinetics 16, 157-333. 
  17. A. Płonka and A. Paszkiewicz (1992), Kinetics in dynamically disorderd systems: Time scale dependence of reaction patterns in condensed media, J. Chem. Phys. 96, 1128-1133. 
  18. S. T. Rachev (1991), Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester. Zbl0744.60004
  19. H. Scher, M. F. Shlesinger and J. T. Bendler (1991), Time-scale invariance in transport and relaxation, Phys. Today 44, 26-34. 
  20. N. G. Van Kampen (1987), Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam. Zbl0511.60038
  21. K. Weron (1991), A probabilistic mechanism hidden behind the universal power law for dielectric relaxation: General relaxation equation, J. Phys.: Condens. Matter 3, 9151-9162. 
  22. K. Weron (1992), Reply to the comment by A. Hunt, ibid. 4, 10507-10512. 
  23. K. Weron and A. Jurlewicz (1993), Two forms of self-similarity as a fundamental feature of the power-law dielectric response, J. Phys. A: Math. Gen. 26, 395-410. 
  24. K. Weron and A. Weron (1987), A statistical approach to relaxation in glassy materials, in: Mathematical Statistics and Probability Theory, Vol. B, P. Bauer et al. (eds.). Reidel, 245-254. Zbl0810.60045
  25. V. M. Zolotariev (1986), One-dimensional Stable Distributions, Amer. Math. Soc., Providence. 

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