Abstract
In this paper, we obtain moderate deviations of random sets which take values of bounded closed convex sets on the underling separable Banach space with respect to the Hausdorff distance d H . We also get moderate deviations for random upper semicontinuous functions whose values are of bounded closed convex levels on the underling separable Banach space in the sense of the uniform Hausdorff distance \({d^{\infty}_{H}}\). The main tool is the work of Wu on the moderate deviations for empirical processes [15].
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Wang, X. (2011). Moderate Deviations of Random Sets and Random Upper Semicontinuous Functions. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_18
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DOI: https://doi.org/10.1007/978-3-642-22833-9_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
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