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On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. (English) Zbl 0611.60004
In Trans. Am. Math. Soc. 266, 275-289 (1981; Zbl 0501.28005) the authors have given various characterizations for the a.s. convergence and the convergence in probability of sequences of closed-valued measurable multifunctions (random closed sets). In the present paper they study their convergence in distribution (weak*-convergence of the induced probability measures) and the epi-convergence in distribution of normal integrands (random lower semicontinuous functions).
The relation between the epi-convergence in distribution and the convergence in the classical sense of stochastic processes is analyzed. As an application a modified derivation of Donsker’s invariance principle is given. The potential application to the study of the convergence of stochastic infima is also suggested.
Reviewer: V.Mackevičius

MSC:
60B10 Convergence of probability measures
90C15 Stochastic programming
60D05 Geometric probability and stochastic geometry
Citations:
Zbl 0501.28005
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