摘要：

The initial-value problem of the one-dimensional wave propagation in a homogeneous random medium is treated by means of the "Laplace transform," based again on a group-theoretic consideration introduced in the preceding paper. We first define the "Fourier transform" of a random process regarded as a function on the translation group associated with the homogeneity. The inverse "Fourier transform" then gives a general representation of a nonstationary random process generated by a stationary process. Similarly, we define the "Laplace transform" of a random process vanishing on the negative coordinate axis as well as the "Laplace transform" of its derivatives. The one-dimensional wave equation together with the random initial values can be directly treated by means of the "Laplace-transform" technique and is solved approximately in two Gaussian cases where the random media are represented by the well-known O-U (Ornstein-Uhlenbeck) process and by the Z₀ process having zero spec

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