Abstract
A random set is a multivalued measurable function defined on a probability space. If this multivalued function depends on the second argument (e.g., time or space), then random processes of sets (set-valued processes or random multivalued functions) appear. Important examples are provided by growth processes, multivalued martingales and solutions of stochastic differential inclusions. If time is discrete, one deals with sequences of random closed sets.
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References
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Molchanov, I. (2017). Random Sets and Random Functions. In: Theory of Random Sets. Probability Theory and Stochastic Modelling, vol 87. Springer, London. https://doi.org/10.1007/978-1-4471-7349-6_5
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