Wave distribution in a variable medium with random inhomogeneities

We consider the behavior of a solution of the wave equation u_tt (t, x) – a² (t) u_xx (t, x)=f (t, x) with initial conditions u (0, x)=u₀, /t6t u (t, x) ¦_t=0=u₁ (x), a andf being random functions; a(t) characteristizes the variable character of the medium;f(t, x) is the inhomogeneity, having the character of random walks.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 75–78, 1988.