  The paper investigates properties of mean-square solutions to the Airy
equation with random initial data given by stationary processes. The result on
the modulus of continiuty of the solution is stated and properties of the
covariance function are described. Bounds for the distributions of the suprema
of solutions under $\varphi$-sub-Gaussian initial conditions are presented.
Several examples are provided to illustrate the results. Extension of the
results to the case of fractional Airy equation is given.
