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Monte Carlo and Quasi-Monte Carlo Methods 1996 pp 300–307Cite as

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

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Part of the book series: Lecture Notes in Statistics ((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.

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Author information

Authors and Affiliations

  1. Hugo Steinhaus Center for Stochastic Methods, Technical University of Wroclaw, Wyspiańskiego 27, Wroclaw, 50-370, Poland

    Marcin Kotulski

Authors
  1. Marcin Kotulski
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Editor information

Editors and Affiliations

  1. Institute of Information Processing, Austrian Academy of Sciences, Vienna, A-1010, Austria

    Harald Niederreiter

  2. Department of Mathematics, University of Salzburg, Salzburg, A-5020, Austria

    Peter Hellekalek , Gerhard Larcher  & Peter Zinterhof ,  & 

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© 1998 Springer Science+Business Media New York

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Kotulski, M. (1998). The rate of convergence to a stable law for the random sum of iid random variables. In: Niederreiter, H., Hellekalek, P., Larcher, G., Zinterhof, P. (eds) Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics, vol 127. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1690-2_20

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  • DOI: https://doi.org/10.1007/978-1-4612-1690-2_20

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98335-6

  • Online ISBN: 978-1-4612-1690-2

  • eBook Packages: Springer Book Archive

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