Approach to Stochastic Lagrangian Integrals and Their Asymptotic Evaluation for Sound Propagation in Continuous Stochastic Media

Abstract

Previously the formal solution of the Eulerian-Lagrangian problem for sound propagation in continuous stochastic media was reframed so that the emphasis on the need for complete knowledge of the statistical nature of the Lagrangian functional of interest is shifted to the need for knowledge of the asymptotic behavior of certain stochastic Lagrangian integrals which result from the application of a central limit theorem for stochastic functionals. In this paper, the asymptotic evaluation of these Lagrangian stochastic integrals is developed and illustrated for both ensemble and subensemble expectations in a statistically isotropic medium. In addition, the relationship between this method of analysis and the comparable Wiener integral is discussed.