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1995-1996 | 23 | 4 | 379-394
Tytuł artykułu

Asymptotic behaviour of stochastic systems with conditionally exponential decay property

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
23
Numer
4
Strony
379-394
Opis fizyczny
Daty
wydano
1996
otrzymano
1994-11-18
poprawiono
1995-09-27
Twórcy
  • Hugo Steinhaus Center for Stochastic Methods, Technical University of Wrocław, 50-370 Wrocław, Poland
  • Institute of Physics, Technical University of Wrocław, 50-370 Wrocław, Poland
autor
  • Institute of Physics, Technical University of Wrocław, 50-370 Wrocław, Poland
Bibliografia
  • P. Billingsley (1979), Probability and Measure, Wiley, New York.
  • L. Breiman (1992), Probability, SIAM, Philadelphia.
  • L. A. Dissado and R. M. Hill (1987), Self-similarity as a fundamental feature of the regression of fluctuations, Chem. Phys. 111, 193-207.
  • W. Feller (1966), An Introduction to Probability and Its Applications, Vol. 2, Wiley, New York.
  • 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.
  • A. Hunt (1994), On the 'universal' scaling of the dielectric relaxation in dipole liquids and glasses, J. Phys.: Condens. Matter, to appear.
  • A. Janicki and A. Weron (1994), Can one see α-stable variables and processes? Statist. Sci. 9, 109-126.
  • A. K. Jonscher (1983), Dielectric Relaxation in Solids, Chelsea Dielectrics, London.
  • 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.
  • J. Klafter, M. F. Shlesinger, G. Zumoffen and A. Blumen (1992), Scale invariance in anomalous diffusion, Phil. Mag. B65, 755-765.
  • M. R. Leadbetter, G. Lindgren and H. Rootzen (1986), Extremes and Related Properties of Random Sequences and Processes, Springer, New York.
  • S. Mittnik and S. T. Rachev (1991), Modelling asset returns with alternative stable distributions, Stony Brook Working Papers WP-91-05 1-63.
  • E. W. Montroll and J. T. Bendler (1984),
  • On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation, J. Statist. Phys. 34, 129-162.
  • 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.
  • A. Płonka (1991), Developments in dispersive kinetics, Prog. Reaction Kinetics 16, 157-333.
  • 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.
  • S. T. Rachev (1991), Probability Metrics and the Stability of Stochastic Models, Wiley, Chichester.
  • H. Scher, M. F. Shlesinger and J. T. Bendler (1991), Time-scale invariance in transport and relaxation, Phys. Today 44, 26-34.
  • N. G. Van Kampen (1987), Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam.
  • 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.
  • K. Weron (1992), Reply to the comment by A. Hunt, ibid. 4, 10507-10512.
  • 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.
  • 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.
  • V. M. Zolotariev (1986), One-dimensional Stable Distributions, Amer. Math. Soc., Providence.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv23i4p379bwm
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