Advertisement

The rate of convergence to a stable law for the random sum of iid random variables

  • Marcin Kotulski
Part of the Lecture Notes in Statistics book series (LNS, volume 127)

Abstract

We investigate, using Monte Carlo method, the rate of convergence to asymptotic distribution for the random sum of iid random variables, known in statistical physics as Continuous-Time Random Walk (CTRW). The rate of convergence, estimated from the simulation, is in agreement with theory. Simulated densities are compared with the limiting Lévy-stable densities.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).CrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Kotulski, J. Stat. Phys. 81 777 (1995).CrossRefzbMATHGoogle Scholar
  3. [3]
    A. Janicki and A. Weron, Simulation and Chaotic Behavior of a-Stable Stochastic Processes, (Marcel Dekker, New York, 1994).Google Scholar
  4. [4]
    V. M. Zolotarev, One-dimensional Stable Distributions, (American Mathematical Society, 1986).zbMATHGoogle Scholar
  5. [5]
    R. N. Pillai, Ann. Inst. Statist. Math. 42 157 (1990).CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    K. Weron and M. Kotulski, Physica A (1996), in press.Google Scholar
  7. [7]
    B. V. Gnedenko, Wiss. Z. Humboldt-Univ. Berlin, Math.-Nat. Reihe 3, 287 (1954).zbMATHGoogle Scholar
  8. [8]
    A. Janssen and D. M. Mason, Probab. Th. Rel. Fields 86 253 (1990).CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    V. Paulauskas, Lith. Math. J. 14 165 (1974).MathSciNetGoogle Scholar
  10. [10]
    W. Macht and W. Wolf, Probab. Th. Rel. Fields 82 295 (1989).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Marcin Kotulski
    • 1
  1. 1.Hugo Steinhaus Center for Stochastic MethodsTechnical University of WroclawWroclawPoland

Personalised recommendations