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1998-1999 | 25 | 4 | 473-488
Tytuł artykułu

Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems arising in science and engineering, often providing a better description of real life phenomena than their Gaussian counterparts.
Rocznik
Tom
25
Numer
4
Strony
473-488
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-08
Twórcy
  • Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland
Bibliografia
  • L. Breiman (1968), (1992), Probability, 1st and 2nd eds., Addison-Wesley, Reading.
  • S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, M. Simons and H. E. Stanley (1993), Generalized Lévy walk model for DNA nucleotide sequences, Phys. Rev. E 47, 4514-4523.
  • P. Embrechts, C. Klüppelberg and T. Mikosch (1997), Modelling Extremal Events, Springer, Berlin.
  • T. S. Ferguson and M. J. Klass (1972), A representation of independent increments processes without Gaussian components, Ann. Math. Statist. 43, 1634-1643.
  • A. Janicki and A. Weron (1994a), Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker, New York.
  • A. Janicki and A. Weron (1994b), Can one see α-stable variables and processes?, Statist. Sci. 9, 109-126.
  • Y. Kasahara and M. Maejima (1986), Functional limit theorems for weighted sums of i.i.d. random variables, Probab. Theory Related Fields 72, 161-183.
  • T. Kurtz and P. Protter (1991), Weak limit theorems for stochastic integrals and stochastic differential equations, Ann. Probab. 19, 1035-1070.
  • M. Ledoux and M. Talagrand (1991), Probability Theory in Banach Spaces, Springer, Berlin.
  • R. LePage (1980), (1989), Multidimensional infinitely divisible variables and processes. Part I: Stable case, Technical Report No. 292, Department of Statistics, Stanford University; in: z Probability Theory on Vector Spaces IV (Łańcut, 1987), S. Cambanis and A. Weron (eds.), Lecture Notes in Math. 1391, Springer, New York, 153-163.
  • W. Linde (1986), Probability in Banach Spaces-Stable and Infinitely Divisible Distributions, Wiley, New York.
  • K. R. Parthasarathy (1967), Probability Measures on Metric Spaces. Academic Press, New York and London.
  • P. Protter (1990), Stochastic Integration and Differential Equations-A New Approach, Springer, New York.
  • J. Rosinski (1990), On series representations of infinitely divisible random vectors, Ann. Probab. 18, 405-430.
  • G. Samorodnitsky and M. Taqqu (1994), Non-Gaussian Stable Processes: Stochastic Models with Infinite Variance, Chapman and Hall, London.
  • M. Shao and C. L. Nikias (1993), z Signal processing with fractional lower order moments: stable processes and their applications, Proc. IEEE 81, 986-1010.
  • X. J. Wang (1992), Dynamical sporadicity and anomalous diffusion in the Lévy motion, Phys. Rev. A 45, 8407-8417.
  • A. Weron (1984), z Stable processes and measures: A survey; in: Probability Theory on Vector Spaces III, D. Szynal and A. Weron (eds.), Lecture Notes in Math. 1080, Springer, New York, 306-364.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i4p473bwm
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