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Nonlinear Stochastic Mechanics pp 267–272Cite as

Probabilistic Methods to Waves in Heterogeneous Media

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Part of the book series: IUTAM Symposia ((IUTAM))

Abstract

This line of work is motivated by our wanting to solve wave equations, to be used for direct modelling in geophysical applications, without having to go thru the wear and tear of numerical grid methods. Here we provide path integral representations for the solution to wave equation (1) which can be the starting point for Montecarlo simulation techniques.

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References

  1. Gzyl, H. and Jiménez, R.: PROBABILISTIC APPROACH TO WAVE PROPAGATION PROBLEMS, I. Mathl. Comput. Modelling, vol 13, n° 11, pp. 57–65, 1990

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  2. Gzyl, H.: PROBABILISTIC APPROACH TO WAVE PROPAGATION PROBLEMS, II: BOUNDARY VALUE PROBLEMS. Mathl. Comput. Modelling, vol 13, n° 11, pp. 67–76, 1990

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  3. Gzyl, H.: PROBABILISTIC APPROACH TO WAVE PROPAGATION PROBLEMS, III: BROWNIAN LOCAL TIMES AND WAVES IN LAYERED MEDIA. Mathl. Comput. Modelling, vol 15, n° 7, pp. 56–62, 1991

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  4. Gzyl, H. and Jiménez, R.: DIFFUSIONS AND WAVES. To appear in J. Math. Anal Appl.

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  5. Betz, C. and Gzyl, H.: PROBABILISTIC APPROACH TO WAVE PROPAGATION PROBLEMS, IV: REFLECTING BOUNDARIES. To appear in Mathl. Comput. Modelling.

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  6. Gzyl, H. and Jiménez, R.: FROM HEAT EQUATIONS TO WAVE EQUATIONS. MORE ON TRANSMUTATION OPERATORS. To appear in Mathl. Comput. Modelling.

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  7. Hsu, P.: BROWNIAN EXIT DISTRIBUTION OF BALL. Seminar Sochastic Processes, Birkhauser, Boston (1985).

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  8. Ermakov, S., Nekrutkin, V. and Sipin, A.: RANDOM PROCESSES FOR CLASSICAL EQUATIONS OF MATHEMATICAL PHYSICS. Kluwer Academic Publishers, Dordrecht (1989).

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Author information

Authors and Affiliations

  1. A.P. 52120, Caracas, 1050 - A, Venezuela

    Henryk Gzyl

  2. A.P. 89000, Caracas, 1080 - A, Venezuela

    Raúl Jiménez

Authors
  1. Henryk Gzyl
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  2. Raúl Jiménez
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129, Torino, Italy

    Nicola Bellomo

  2. Dept. of Structural Mechanics, University of Pavia, Via Abbiategrasso 211, I-27100, Pavia, Italy

    Fabio Casciati

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© 1992 Springer-Verlag Berlin Heidelberg

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Gzyl, H., Jiménez, R. (1992). Probabilistic Methods to Waves in Heterogeneous Media. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_23

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  • DOI: https://doi.org/10.1007/978-3-642-84789-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84791-2

  • Online ISBN: 978-3-642-84789-9

  • eBook Packages: Springer Book Archive

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