Central Limit Theory for Multivalued Mappings

King, A.J. (1987). Central Limit Theory for Multivalued Mappings. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-87-112

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Abstract

This paper presents new fundamental results concerning central limit behavior of sequences of random closed sets, modeled as a multivalued mapping of an underlying asymptotically normal sequence of random variables.

The main theorem generalizes the classical result for differentiable functions in a mathematically satisfying way by combining recent developments in convergence theory for random closed sets and recent work in pseudo-differentiability of multifunctions. Potential applications to the asymptotic analysis of solution sets for stochastic and ordinary parametric programs with incomplete information are indicated in the examples.

This paper reports research that was partly performed in the Adaptation and Optimization Project of the System and Decision Sciences Program.

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