Computer-aided modeling and simulation of electrical circuits with α-stable noise

Aleksander Weron

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 1, page 83-93
  • ISSN: 1233-7234

Abstract

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The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.

How to cite

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Weron, Aleksander. "Computer-aided modeling and simulation of electrical circuits with α-stable noise." Applicationes Mathematicae 23.1 (1995): 83-93. <http://eudml.org/doc/219118>.

@article{Weron1995,
abstract = {The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.},
author = {Weron, Aleksander},
journal = {Applicationes Mathematicae},
keywords = {density and quantile estimators; stochastic differential equations; approximate schemes; α-stable random variables and processes; stochastic modeling; stable random variables and processes},
language = {eng},
number = {1},
pages = {83-93},
title = {Computer-aided modeling and simulation of electrical circuits with α-stable noise},
url = {http://eudml.org/doc/219118},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Weron, Aleksander
TI - Computer-aided modeling and simulation of electrical circuits with α-stable noise
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 1
SP - 83
EP - 93
AB - The aim of this paper is to demonstrate how the appropriate numerical, statistical and computer techniques can be successfully applied to the construction of approximate solutions of stochastic differential equations modeling some engineering systems subject to large disturbances. In particular, the evolution in time of densities of stochastic processes solving such problems is discussed.
LA - eng
KW - density and quantile estimators; stochastic differential equations; approximate schemes; α-stable random variables and processes; stochastic modeling; stable random variables and processes
UR - http://eudml.org/doc/219118
ER -

References

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  1. J. Berger and B. Mandelbrot (1963), A new model for error clustering in telephone circuits, IBM J. Res. and Develop. 7, 224-236. 
  2. L. M. Berliner (1992), Statistics, probability and chaos, Statist. Sci. 7, 69-90. Zbl0955.62520
  3. J. M. Chambers, C. L. Mallows and B. Stuck (1976), A method for simulating stable random variables, J. Amer. Statist. Assoc. 71, 340-344. Zbl0341.65003
  4. S. Chatterjee and M. R. Yilmaz (1992), Chaos, fractals and statistics, ibid. 7, 49-68. Zbl0955.37500
  5. L. Devroye (1987), A Course in Density Estimation, Birkhäuser, Boston. Zbl0617.62043
  6. L. Gajek and A. Lenic (1993), An approximate necessary condition for the optimal bandwidth selector in kernel density estimation, Applicationes Math. 22, 123-138. Zbl0789.62028
  7. C. W. Gardiner (1983), Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer, New York. Zbl0515.60002
  8. W. Härdle, P. Hall and J. S. Marron (1988), How far are automatically chosen regression smoothing parameters from their optimum? (with comments), J. Amer. Statist. Assoc. 74, 105-131. Zbl0644.62048
  9. A. Janicki (1995), Computer simulation of a nonlinear model for electrical circuits with α-stable noise, this volume, 95-105. Zbl0822.60051
  10. A. Janicki, Z. Michna and A. Weron (1994), Approximation of stochastic differential equations driven by α-stable Lévy motion, preprint. Zbl0879.60059
  11. A. Janicki and A. Weron (1994), Can one see α-stable variables and processes?, Statist. Sci. 9, 109-126. Zbl0955.60508
  12. A. Janicki and A. Weron (1994a), Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker, New York. Zbl0946.60028
  13. M. Kanter (1975), Stable densities under change of scale and total variation inequalities, Ann. Probab. 31, 697-707. Zbl0323.60013
  14. A. Lasota and M. C. Mackey (1994), Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics, Springer, New York. Zbl0784.58005
  15. B. Mandelbrot and J. W. van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10, 422-437. Zbl0179.47801
  16. M. Shao and C. L. Nikias (1993), Signal processing with fractional lower order moments: stable processes and their applications, Proc. IEEE 81, 986-1010. 
  17. B. W. Stuck and B. Kleiner (1974), A statistical analysis of telephone noise, Bell Syst. Tech. J. 53, 1263-1320. 
  18. A. Weron (1984), 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. 

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