Dynamic programming, Fermat's principle and stochastic Eikonal equations

Abstract

An extension of Fermat's principle to the stochastic case is presented in order to treat ray propagation in random media. The concept of dynamic programming permits one to derive a sequence of stochastic eikonal equations from which a sequence of rays can be traced using Hamilton's equations. The extension is motivated by analogous stochastic control problems in which the concepts and methods are adapted to the present problem. To facilitate understanding of the main ideas the presentation is given in a simple and somewhat naive manner. Two simple examples are presented to demonstrate the ideas and techniques.