A Formula on the Hermite Expansion and Its Application to a Random Boundary Value Problem

Yasuhiko TAMURA  Junichi NAKAYAMA  

IEICE TRANSACTIONS on Electronics   Vol.E86-C   No.8   pp.1743-1748
Publication Date: 2003/08/01
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Electromagnetic Theory
Hermite expansion,  random boundary value problem,  stochastic analysis,  exact solution,  

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A new formula on the Hermite expansion is presented in an explicit form. An application of the formula is given to a random boundary value problem: a plane wave reflection from a flat plane, of which position is randomly distributed in the normal direction, is presented. Several numerical results are given for a verification of the formula and for a discussion of the exact behavior of the fluctuation part of the reflection power.