Random Set Solutions to Stochastic Wave Equations

Michael Oberguggenberger; Lukas Wurzer

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arXiv · 1903.06543

Random Set Solutions to Stochastic Wave Equations

Michael Oberguggenberger·Lukas Wurzer

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Abstract

This paper is devoted to three topics. First, proving 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 arbitrary space dimensions; and third, to computing upper and lower probabilities of the values of the solution in the case of one space dimension.

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BibTeX RIS

Michael Oberguggenberger, Lukas Wurzer. 2019-03-15. Random Set Solutions to Stochastic Wave Equations. https://arxiv.org/abs/1903.06543

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