Random Set Solutions to Stochastic Wave Equations
Probability
2019-03-18 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1903.06543,
title = {Random Set Solutions to Stochastic Wave Equations},
author = {Michael Oberguggenberger and Lukas Wurzer},
journal= {arXiv preprint arXiv:1903.06543},
year = {2019}
}