Set-Valued Stochastic Processes and Sets of Probability Measures Induced by Stochastic Differential Equations with Random Set Parameters

We consider stochastic differential equations depending on parameters whose uncertainty is modeled by random compact sets. Several approaches are discussed how to construct set-valued processes from the solutions. The induced lower and upper probabilities are compared to a set of probability measures constructed from the distributions of the solutions and the selections of the random set.

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