Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions
Volume 7, Issue 1 (2020), pp. 79–96
Pub. online: 17 December 2019
Type: Research Article
Open Access
Open Access
Received
25 July 2019
25 July 2019
Revised
10 October 2019
10 October 2019
Accepted
16 November 2019
16 November 2019
Published
17 December 2019
17 December 2019
Abstract
In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.
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