Random LSC Functions: An Ergodic Theorem
Published Online:1 May 2001https://doi.org/10.1287/moor.26.2.421.10548
References
- Consistency of minimizers and the SLLN for stochastic programs. J. Convex Anal. (1995) 2:1–17Google Scholar
- Variational Convergence for Functions and Operators (1984) (Pitman)Applicable Mathematics SeriesGoogle Scholar
- Epigraphical processes: laws of large numbers for random lsc functions. Sém. Anal. Convexe, Montepellier (1990) 13.1–13.29Google Scholar
- Stochastic homogenization and ergodic theory. (1999) . Manuscript, University of California, DavisGoogle Scholar
- Set-Valued Analysis (1990) (Birkhäuser Boston Inc., Boston, MA) Google Scholar
- Statistical Inference Under Order Restrictions. The Theory and Application of Isotonic Regression (1972) (John Wiley & Sons, London) Wiley Series in Probability and StatisticsGoogle Scholar
- A polish topology for the closed subsets of a polish space. Proc. Amer. Math. Soc. (1991a) 113:1123–1133Crossref, Google Scholar
- Topologies on closed and closed convex sets and the Effrös measurability of set valued functions. Sém. Anal. Convexe, Montepellier (1991b) 21–2Google Scholar
- Topologies on Closed and Closed Convex Sets (1993) (Kluwer Academic Publishers, Dordrecht) Crossref, Google Scholar
- Introduction to Stochastic Programming (1997) (Springer, New York) Google Scholar
- Least Absolute Deviations: Theory, Applications and Algorithms (1983) (Birkhäuser Boston Inc., Boston, MA) Google Scholar
- Time Series Analysis Forecasting and Control (1970) (Holden-Day)Google Scholar
- SLLN for convex random sets and random lower semicontinuous integrands. (1995) . Manuscript, Université de MontpellierGoogle Scholar
- Convex Analysis and Measurable Multifunctions (1977) (Springer, Berlin) Lecture Notes in Mathematics 580Crossref, Google Scholar
- Outils topologiques et métriques de l'analyse mathematique. (1966) (Centre de documentation universitaire et SEDES réunis, Paris) Lecture NotesGoogle Scholar
- Théorème ergodique ponctuel et lois fortes des grands nombres pour des points aléatoires d'un espace métrique á courbure négative. Ann. Probab. (1997) 25:738–766Crossref, Google Scholar
- Probability: Theory and Examples (1991) (Wadsworth & Brooks/Cole)Google Scholar
- Convergence of closed subsets in a topological space. Proceedings of the American Mathematical Society (1965) 16:929–931Crossref, Google Scholar
- A Hausdorff topology for the closed subsets of a locally compact Hausdorff space. Proceedings of the American Mathematical Society (1962) 13:472–476Crossref, Google Scholar
- Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions. J. Math. Anal. Appl. (1985) 112:347–370Crossref, Google Scholar
- 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
- Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. Ann. Statist. (1996) 24(3):1298–1315Crossref, Google Scholar
- Measurable relations. Fundamenta Mathematicae (1975) 87:52–72Crossref, Google Scholar
- Stochastic Programming (1994) (Wiley, Chichester) Google Scholar
- 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
- Lake eutrophication management: the lake Balaton project. Numerical Techniques for Stochastic Optimization (1988) (Springer, Berlin) 435–444Crossref, Google Scholar
- Random lsc functions: An ergodic theorem. (2000a) . http://dochost.rz.hu-berlin.de/spepsGoogle Scholar
- Random lsc functions: Scalarization. (2000b) . http://dochost.rz.hu-berlin.de/speps, 2000Google Scholar
- Homogenization of Differential Operators and Integral Functionals (1994) (Springer, Berlin) Google Scholar
- Probability Theory II (1978) 4th ed.(Springer, New York) Crossref, Google Scholar
- , 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
- Probability Measures on Metric Spaces (1967) (Academic Press, New York) Crossref, Google Scholar
- Order-Restricted Statistical Inference (1988) (John Wiley & Sons, Chichester) Wiley Series in Probability and StatisticsGoogle Scholar
- , 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. 543Crossref, Google Scholar
- , 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) 1–54Crossref, Google Scholar
- Variational Analysis (1998) (Springer)Crossref, Google Scholar
- On the convergence in distribution of measurable multifunctions (random sets), normal integrands, stochastic processes and stochastic infima. Math. Oper. Res. (1986) 11:385–419Link, Google Scholar
- A splitting algorithm for multistage stochastic programming with application to hydropower scheduling (1997) . Ph.d. thesis, University of Washington, SeattleGoogle Scholar
- , 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) 85–118Crossref, Google Scholar
- Random upper semicontinuous functions and extremal processes. (1988) . Report MS-R8801, Center for Wiskunde en Informatica, Amsterdam, The NetherlandsGoogle Scholar
- On stability in stochastic programming-sufficient conditions for continuous convergence and epi-convergence. (1995) . TU Ilmenau, Inst. Math. ForthcomingGoogle Scholar
- , 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
- Convergence of sequences of convex sets, cones, and functions, ii. Trans. Amer. Math. Soc. (1966) 123:32–45Crossref, Google Scholar

