Symbolic computing in probabilistic and stochastic analysis

Marcin Kamiński

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 4, page 961-973
  • ISSN: 1641-876X

Abstract

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The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.

How to cite

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Marcin Kamiński. "Symbolic computing in probabilistic and stochastic analysis." International Journal of Applied Mathematics and Computer Science 25.4 (2015): 961-973. <http://eudml.org/doc/275924>.

@article{MarcinKamiński2015,
abstract = {The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.},
author = {Marcin Kamiński},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {probabilistic analysis; stochastic computer methods; symbolic computation},
language = {eng},
number = {4},
pages = {961-973},
title = {Symbolic computing in probabilistic and stochastic analysis},
url = {http://eudml.org/doc/275924},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Marcin Kamiński
TI - Symbolic computing in probabilistic and stochastic analysis
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 4
SP - 961
EP - 973
AB - The main aim is to present recent developments in applications of symbolic computing in probabilistic and stochastic analysis, and this is done using the example of the well-known MAPLE system. The key theoretical methods discussed are (i) analytical derivations, (ii) the classical Monte-Carlo simulation approach, (iii) the stochastic perturbation technique, as well as (iv) some semi-analytical approaches. It is demonstrated in particular how to engage the basic symbolic tools implemented in any system to derive the basic equations for the stochastic perturbation technique and how to make an efficient implementation of the semi-analytical methods using an automatic differentiation and integration provided by the computer algebra program itself. The second important illustration is probabilistic extension of the finite element and finite difference methods coded in MAPLE, showing how to solve boundary value problems with random parameters in the environment of symbolic computing. The response function method belongs to the third group, where interference of classical deterministic software with the non-linear fitting numerical techniques available in various symbolic environments is displayed. We recover in this context the probabilistic structural response in engineering systems and show how to solve partial differential equations including Gaussian randomness in their coefficients.
LA - eng
KW - probabilistic analysis; stochastic computer methods; symbolic computation
UR - http://eudml.org/doc/275924
ER -

References

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