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Arnab Sur(arnabsur2002gmail.com) Abstract: The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semicontinuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$almost all starting points. The property of Harris recurrence allows us to replace ``almost all" by ``all", which is potentially important when running Markov chain Monte Carlo algorithms. That result on epiconvergence is then applied to establish the consistency of the optimal solutions and optimal value of a stochastic optimization problem involving expectation functional of the form $ E_{\pi}[f(x,\xi)].$ Moreover, we develop asymptotic normality of the statistical estimator of the optimal value using a Markov chain central limit theorem. Keywords: Sample average approximation method, Epigraphical convergence, Random lower semicontinuous function, Measurepreserving ergodic transformation, Harris recurrent Markov chain, Consistency, Asymptotic normality. Category 1: Stochastic Programming Citation: MOR2020092, The University of Chicago, March/2020 Download: [PDF] Entry Submitted: 04/21/2020 Modify/Update this entry  
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