STOCHASTIC ANALYSIS IN THE ACOUSTICS OF DAMPED SOUNDS

Authors

  • Tadeusz Banek Lublin Technical University

DOI:

https://doi.org/10.7494/mech.2014.33.1.1

Keywords:

Acoustic signal processing, Feynman-Kac formula, Acoustic statistical characteristic, Stochastic processes

Abstract

A stochastic model of sound propagation in damping medium is proposed. It consists of: (1) Ito’s stochastic differential equation describing the sound propagation, (2) a potential which models the damping effects. However, due to presence of path integrals this model is elaborate and time consuming, hence inappropriate for numerical simulations and/or model calibrations. To make it simpler we usde the classical results of stochastic analysis; Feynman-Kac formula and Girsanov tansformation obtaining easy-to-use computational procedure for practical purposes.

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References

Bakhtin Y., Mueller C., 2010, Solutions of semilinear wave equation via stochastic cascades. Commun. Stoch. Anal. 4, No. 3, 425–431.

Chatterjee S., 2013, http://arxiv.org/pdf/1306.2382.pdf.

Dalang R., Mueller C., Tribe R. 2008, A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.’s. Trans. Amer. Math. Soc. 360, No. 9, 4681–4703.

Ito K., McKean H.P. Jr, 1970, Diffusion processes and their sample paths. Springer.

Karatzas I., Shreve S.E., 1991, Brownian Mation and Stochastic Calculus. Springer-Verlag.

Pal S., Shkolnikov M., 2013, http://arxiv.org/abs/1306.0857.

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Published

2015-05-04

Issue

Vol. 33 No. 1 (2014)

Section

Articles

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