Abstract
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 continuity of the solution is stated and properties of the covariance function are described. Bounds for the distributions of the suprema of solutions under φ-sub-Gaussian initial conditions are presented. Several examples are provided to illustrate the results. Possible extensions of the results are discussed.
Acknowledgments
The author is grateful to the reviewers for their valuable remarks and suggestions, which helped to improve the paper significantly.
Citation
Lyudmyla Sakhno. "Investigation of Airy equations with random initial conditions." Electron. Commun. Probab. 28 1 - 14, 2023. https://doi.org/10.1214/23-ECP522
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