Diffusions and Waves by Henryk GzylDiffusions and Waves by Henryk Gzyl

Diffusions and Waves

byHenryk Gzyl

Paperback | October 21, 2012

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In this book several connections between probability theory and wave propagation are explored. The connection comes via the probabilistic (or path integral) representation of both the (fixed frequency) Green functions and of the propagators -operators mapping initial into present time data. The formalism includes both waves in continuous space and in discrete structures.
One of the main applications of the formalism developed is to inverse problems in wave propagation. Using the probabilistic formalism, the parameters of the medium and the surfaces determining the region of propagation appear explicitly in the path integral representation of the Green functions and propagators. This fact is what provides a useful starting point for inverse problem formulation.

Audience:The book is suitable for advanced graduate students in the mathematical, physical or in the engineering sciences. The presentation is quite self-contained, and not extremely rigorous.

Title:Diffusions and WavesFormat:PaperbackDimensions:236 pages, 24 × 16 × 0.01 inPublished:October 21, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401039496

ISBN - 13:9789401039499

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Table of Contents

Introduction. 1. Basic Probabilistic Notions. 2. From Brownian Motion to Diffusions. 3. Waves. 4. Waves and Brownian Motions. 5. Waves and Diffusions. 6. Asymptotic Expansions. 7. Transmutation Operations. 8. More Connections. 9. Applications. Subject Index.