Stochastic turning point problem in a one-dimensional refractive random multilayer

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Abstract

A one-dimensional model of random scattering is considered for a totally refracting random multilayer that has two separated spatial scales, i.e., deterministic macroscale and random microscale. The interplay of internal refraction and random multiple scattering for a turning point problem is analyzed with an intermediate scale of the wavelength. Two extended limit theorems for stochastic differential equations with a small parameter provide the characterization of the diffusion processes above and below the turning point. Both results are combined, and a global limit law for the phenomenon of the random phase is obtained.

Original languageEnglish
Pages (from-to)1164-1180
Number of pages17
JournalSIAM Journal on Applied Mathematics
Volume56
Issue number4
DOIs
Publication statusPublished - 1996 Aug

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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