The Annals of Applied Probability

A general framework for waves in random media with long-range correlations

Renaud Marty and Knut Sølna

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Abstract

We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in [19] and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this paper, we prove in particular that the asymptotic time-shift can be described in terms of non-Gaussian and/or multifractal processes.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 1 (2011), 115-139.

Dates
First available in Project Euclid: 17 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1292598029

Digital Object Identifier
doi:10.1214/10-AAP689

Mathematical Reviews number (MathSciNet)
MR2759197

Zentralblatt MATH identifier
1223.34085

Subjects
Primary: 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03] 34E10: Perturbations, asymptotics 37H10: Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 60H20: Stochastic integral equations

Keywords
Waves in random media long-range dependence fractional and multifractional processes

Citation

Marty, Renaud; Sølna, Knut. A general framework for waves in random media with long-range correlations. Ann. Appl. Probab. 21 (2011), no. 1, 115--139. doi:10.1214/10-AAP689. https://projecteuclid.org/euclid.aoap/1292598029


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