Random Set Solutions to Stochastic Wave Equations

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Michael Oberguggenberger, Lukas Wurzer ;
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:314-323, 2019.

Abstract

This paper is devoted to three topics. First, to prove a measurability theorem for multifunctions with values in non-metrizable spaces, which is required to show that solutions to stochastic wave equations with interval parameters are random sets; second, to apply the theorem to wave equations in any space dimension; and third, to compute upper and lower probabilities of the values of the solution in the case of one space dimension.

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