We consider a boundary value problem for the telegraph equation in a strip and study the existence of solutions periodic in the following sense. The equation contains random periodic perturbations; periodicity is understood as time periodicity only of averaged characteristics of the perturbation and the solution of the boundary value problem. For a solution periodic in this sense, trajectories-realizations can be aperiodic functions with probability 1. The deterministic situation can be analyzed in a similar way; by way of example, we present a theorem similar to the results in [1, p. 133]. The existence of periodic solutions of deterministic partial differential equations has been comprehensively analyzed (e.g., see the monograph [1], which deals solely with periodic solutions of partial differential equations and also contains applications). The existence of stationary solutions, as well as solutions periodic in distribution, of ordinary stochastic equations has also been considered by numerous authors (see [2, 3] and the survey [4], where a detailed bibliography is given). In addition, note that the analysis of stochastic partial differential equations attracts the attention of mathematicians as well as specialists in applied sciences (e.g., see [5-9] and references therein). The results of the present paper have been obtained with the use of [10] under simple assumptions imposed on the random perturbations.
