Continuity of imprecise stochastic processes with respect to the pointwise convergence of monotone sequences

2014/02/13 by Jasper De Bock, De Bock, Jasper, Gert de Cooman +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1402.3056

arxiv created 2017/01/25 · arxiv updated 2017/01/26

Abstract

We consider the joint lower expectation of a finite-state imprecise stochastic process, defined using either the Ville-Vovk-Shafer natural extension or the Williams natural extension. In both cases, we show that it is continuous with respect to the pointwise convergence of non-decreasing sequences of real-valued functions f_n, n∈ℕ₀, where each f_n is n-measurable. For the Ville-Vovk-Shafer natural extension, a similar result is shown to hold for non-increasing sequences, provided that they converge to a bounded function.

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