Random Set Solutions to Stochastic Wave Equations

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-oberguggenberger19a, title = {Random Set Solutions to Stochastic Wave Equations}, author = {Oberguggenberger, Michael and Wurzer, Lukas}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {314--323}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/oberguggenberger19a/oberguggenberger19a.pdf}, url = {https://proceedings.mlr.press/v103/oberguggenberger19a.html}, 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.} }
Endnote
%0 Conference Paper %T Random Set Solutions to Stochastic Wave Equations %A Michael Oberguggenberger %A Lukas Wurzer %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-oberguggenberger19a %I PMLR %P 314--323 %U https://proceedings.mlr.press/v103/oberguggenberger19a.html %V 103 %X 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.
APA
Oberguggenberger, M. & Wurzer, L.. (2019). Random Set Solutions to Stochastic Wave Equations. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:314-323 Available from https://proceedings.mlr.press/v103/oberguggenberger19a.html.

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