Can One See Alpha-stable Variables and Processes?

Aleksander Janicki and Aleksander Weron

No HSC/94/01, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: In this paper, we demonstrate some properties of Alpha-stable (stable) random variables and processes. It turns out that with the use of suitable statistical estimation techniques, computer simulation procedures and numerical discretization methods it is possible to construct approximations of stochastic integrals with stable measures as integrators. As a consequence we obtain an effective, general method giving approximate solutions for a wide class of stochastic differential equations involving such integrals. Application of computer graphics provides interesting quantitative and visual information on those features of stable variates which distinguish them from their commonly used Gaussian counterparts. It is possible to demonstrate evolution in time of densities with heavy tails of appropriate processes, to visualize the effect of jumps of trajectories, etc. We try to demonstrate that stable variates can be very useful in stochastic modeling of problems of different kinds, arising in science and engineering, which often provide better description of real life phenomena than their Gaussian counterparts.

Keywords: Stable distributions; stable processes; stochastic integrals; statistical estimation; stochatic modeling; computer simulation (search for similar items in EconPapers)
Pages: 18 pages
Date: 1994
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Citations: View citations in EconPapers (8)

Published in Statistical Science 9(1) (1994) 109-126

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Persistent link: https://EconPapers.repec.org/RePEc:wuu:wpaper:hsc9401

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