Random Set Solutions to Stochastic Wave Equations
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Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:314323, 2019.
Abstract
This paper is devoted to three topics. First, to prove a measurability theorem for multifunctions with values in nonmetrizable 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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