Computer simulation of a nonlinear model for electrical circuits with α-stable noise

Aleksander Janicki

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 1, page 95-105
  • ISSN: 1233-7234

Abstract

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The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.

How to cite

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Janicki, Aleksander. "Computer simulation of a nonlinear model for electrical circuits with α-stable noise." Applicationes Mathematicae 23.1 (1995): 95-105. <http://eudml.org/doc/219119>.

@article{Janicki1995,
abstract = {The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.},
author = {Janicki, Aleksander},
journal = {Applicationes Mathematicae},
keywords = {density and quantile estimators; approximate schemes; stochastic differential equations with α-stable integrators; stochastic modeling; computer simulation; stochastic differential equations; large random external disturbances; asymptotic behavior},
language = {eng},
number = {1},
pages = {95-105},
title = {Computer simulation of a nonlinear model for electrical circuits with α-stable noise},
url = {http://eudml.org/doc/219119},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Janicki, Aleksander
TI - Computer simulation of a nonlinear model for electrical circuits with α-stable noise
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 1
SP - 95
EP - 105
AB - The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.
LA - eng
KW - density and quantile estimators; approximate schemes; stochastic differential equations with α-stable integrators; stochastic modeling; computer simulation; stochastic differential equations; large random external disturbances; asymptotic behavior
UR - http://eudml.org/doc/219119
ER -

References

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  1. C. W. Gardiner (1983), Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer, New York. Zbl0515.60002
  2. A. Janicki, Z. Michna and A. Weron (1994), Approximation of stochastic differential equations driven by α-stable Lévy motion, preprint. Zbl0879.60059
  3. A. Janicki and A. Weron (1994), Can one see α-stable variables and processes?, Statist. Sci. 9, 109-126. Zbl0955.60508
  4. A. Janicki and A. Weron (1994a), Simulation and Chaotic Behavior of α-Stable Stochastic Processes, Marcel Dekker, New York. Zbl0946.60028
  5. B. Mandelbrot and J. W. van Ness (1968), Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10, 422-437. Zbl0179.47801
  6. M. Shao and C. L. Nikias (1993), Signal processing with fractional lower order moments: stable processes and their applications, Proc. IEEE 81, 986-1010. 
  7. B. W. Stuck and B. Kleiner (1974), A statistical analysis of telephone noise, Bell Syst. Tech. J. 53, 1263-1320. 
  8. 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. 
  9. A. Weron (1995), Computer-aided modeling and simulation of electrical circuits with α-stable noise, this volume, 83-93. Zbl0823.60048

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