Abstract
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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Schmelzer, B. (2010). Set-Valued Stochastic Processes and Sets of Probability Measures Induced by Stochastic Differential Equations with Random Set Parameters. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_69
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DOI: https://doi.org/10.1007/978-3-642-14746-3_69
Publisher Name: Springer, Berlin, Heidelberg
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