Random LSC Functions: An Ergodic Theorem

References

  • Artstein Z., Wets R. J.-B. Consistency of minimizers and the SLLN for stochastic programs. J. Convex Anal. (1995) 2:1–17Google Scholar
  • Attouch H.Variational Convergence for Functions and Operators (1984) (Pitman)Applicable Mathematics SeriesGoogle Scholar
  • Attouch H., Wets R. J.-B. Epigraphical processes: laws of large numbers for random lsc functions. Sém. Anal. Convexe, Montepellier (1990) 13.1–13.29Google Scholar
  • Attouch H., Licht C., Wets R. J.-B. Stochastic homogenization and ergodic theory. (1999) . Manuscript, University of California, DavisGoogle Scholar
  • Aubin J.-P., Frankowska H.Set-Valued Analysis (1990) (Birkhäuser Boston Inc., Boston, MA) Google Scholar
  • Barlow R., Bartholomew D., Bremmer J., Brunk H.Statistical Inference Under Order Restrictions. The Theory and Application of Isotonic Regression (1972) (John Wiley & Sons, London) Wiley Series in Probability and StatisticsGoogle Scholar
  • Beer G. A polish topology for the closed subsets of a polish space. Proc. Amer. Math. Soc. (1991a) 113:1123–1133CrossrefGoogle Scholar
  • Beer G. Topologies on closed and closed convex sets and the Effrös measurability of set valued functions. Sém. Anal. Convexe, Montepellier (1991b) 21–2Google Scholar
  • Beer G.Topologies on Closed and Closed Convex Sets (1993) (Kluwer Academic Publishers, Dordrecht) CrossrefGoogle Scholar
  • Birge J., Louveaux F.Introduction to Stochastic Programming (1997) (Springer, New York) Google Scholar
  • Bloomfield P., Steiger W. L.Least Absolute Deviations: Theory, Applications and Algorithms (1983) (Birkhäuser Boston Inc., Boston, MA) Google Scholar
  • Box G. E. P., Jenkins G. M.Time Series Analysis Forecasting and Control (1970) (Holden-Day)Google Scholar
  • Castaing C., Ezzaki F. SLLN for convex random sets and random lower semicontinuous integrands. (1995) . Manuscript, Université de MontpellierGoogle Scholar
  • Castaing C., Valadier M.Convex Analysis and Measurable Multifunctions (1977) (Springer, Berlin) Lecture Notes in Mathematics 580CrossrefGoogle Scholar
  • Choquet G. Outils topologiques et métriques de l'analyse mathematique. (1966) (Centre de documentation universitaire et SEDES réunis, Paris) Lecture NotesGoogle Scholar
  • de Fitte P. R. Théorème ergodique ponctuel et lois fortes des grands nombres pour des points aléatoires d'un espace métrique á courbure négative. Ann. Probab. (1997) 25:738–766CrossrefGoogle Scholar
  • Durrett R.Probability: Theory and Examples (1991) (Wadsworth & Brooks/Cole)Google Scholar
  • Effrös E. Convergence of closed subsets in a topological space. Proceedings of the American Mathematical Society (1965) 16:929–931CrossrefGoogle Scholar
  • Fell J. A Hausdorff topology for the closed subsets of a locally compact Hausdorff space. Proceedings of the American Mathematical Society (1962) 13:472–476CrossrefGoogle Scholar
  • Francaviglia S., Lechicki A., Levi S. Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions. J. Math. Anal. Appl. (1985) 112:347–370CrossrefGoogle Scholar
  • Hess C.Contributions á l'étude de la mesurabilité, de la loi de probabilité, et de la convergence de multifonctions (1986) (Thèse d'état, Université de Montpellier II) Google Scholar
  • Hess C. Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. Ann. Statist. (1996) 24(3):1298–1315CrossrefGoogle Scholar
  • Himmelberg C. J. Measurable relations. Fundamenta Mathematicae (1975) 87:52–72CrossrefGoogle Scholar
  • Kall P., Wallace S.Stochastic Programming (1994) (Wiley, Chichester) Google Scholar
  • Kaňková V. Optimum solution of a stochastic optimization problem with unknown parameters. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, and of the 1974 European Meeting of Statisticians, B (1978) 239–244Google Scholar
  • King A., Rockafellar R. T., Somlyódy L., Wets R. J.-B., Ermoliev Y., Wets R. Lake eutrophication management: the lake Balaton project. Numerical Techniques for Stochastic Optimization (1988) (Springer, Berlin) 435–444CrossrefGoogle Scholar
  • Korf L. A., Wets R. J.-B. Random lsc functions: An ergodic theorem. (2000a) . http://dochost.rz.hu-berlin.de/spepsGoogle Scholar
  • Korf L. A., Wets R. J.-B. Random lsc functions: Scalarization. (2000b) . http://dochost.rz.hu-berlin.de/speps, 2000Google Scholar
  • Kozlov S., Oleinik O., Zhikov V.Homogenization of Differential Operators and Integral Functionals (1994) (Springer, Berlin) Google Scholar
  • Loève M.Probability Theory II (1978) 4th ed.(Springer, New York) CrossrefGoogle Scholar
  • Papanicolaou G. C., Varadhan S. R., Fritz J., Lebowitz J. L., Szasz D. Boundary value problems with rapidly oscillating random coefficients. Random Fields, volume 27 of Colloquia Mathematica Scoietatis Janos Bolyai (1981) (North Holland)835–873Google Scholar
  • Parthasarathy K. R.Probability Measures on Metric Spaces (1967) (Academic Press, New York) CrossrefGoogle Scholar
  • Robertson T., Wright F., Dykstra R.Order-Restricted Statistical Inference (1988) (John Wiley & Sons, Chichester) Wiley Series in Probability and StatisticsGoogle Scholar
  • Rockafellar R. T., Gossez J., Waelbroeck L. Integral functionals, normal integrands and measurable selections. Nonlinear Operators and the Calculus of Variations (1976) (Springer)157–207Lecture Notes in Mathematics No. 543CrossrefGoogle Scholar
  • Rockafellar R. T., Wets R. J.-B., Salinetti G. Variational systems, an introduction. Multifunctions and Integrands: Stochastic Analysis, Approximation and Optimization, volume 1091 of Lecture Notes in Mathematics (1984) (Springer Verlag, Berlin) 1–54CrossrefGoogle Scholar
  • Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer)CrossrefGoogle Scholar
  • Salinetti G., Wets R. J.-B. On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. Math. Oper. Res. (1986) 11:385–419LinkGoogle Scholar
  • Salinger D.A splitting algorithm for multistage stochastic programming with application to hydropower scheduling (1997) . Ph.d. thesis, University of Washington, SeattleGoogle Scholar
  • Tiao G. C., Hannan E. J., Krishnaiah P. R., Rao M. M. Autoregressive moving average models, intervention problems and outlier detection in times series. Times Series in the Time Domain, volume 5 of Handbook of Statistics (1985) (Elsevier Science Publishers, New York) 85–118CrossrefGoogle Scholar
  • Vervaat W. Random upper semicontinuous functions and extremal processes. (1988) . Report MS-R8801, Center for Wiskunde en Informatica, Amsterdam, The NetherlandsGoogle Scholar
  • Vogel S. On stability in stochastic programming-sufficient conditions for continuous convergence and epi-convergence. (1995) . TU Ilmenau, Inst. Math. ForthcomingGoogle Scholar
  • Wets R. J.-B., Rinnooy Kan A., Nemhauser G., Todd M. Stochastic programming. Optimization, Handbook for Operations Research and Management Sciences (1989) 1(North Holland, New York) 573–629Google Scholar
  • Wijsman R. Convergence of sequences of convex sets, cones, and functions, ii. Trans. Amer. Math. Soc. (1966) 123:32–45CrossrefGoogle Scholar
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