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In the paper we consider higher-order partial differential equations from theclass of linear dispersive equations. We investigate solutions to theseequations subject to random initial conditions given by harmonizable$\varphi$-sub-Gaussian processes. The main results are the bounds for thedistributions of the suprema for solutions. We present the examples ofprocesses for which the assumptions of the general result are verified andbounds are written in the explicit form. The main result is also specified forthe case of Gaussian initial condition.

Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions