The Preservation of Continuity and Lipschitz Continuity by Optimal Reward Operators

References

• Attouch H.Variational Convergence for Functions and Operators (1984) (Pitman Publishing Limited, London, U.K.) Google Scholar
• Dubins L. E., Savage L. J.Inequalities for Stochastic Processes (1965) (McGraw-Hill, New York) . 2nd ed., 1976, DoverGoogle Scholar
• Dubins L. E., Sudderth W. D. Countably additive gambling and optimal stopping. Z. Wahr. v. Geb. (1977) 41:59–72Crossref, Google Scholar
• Dubins L. E., Maitra A. P., Sudderth W. D., Feinberg E. A., Shwartz A. Invariant gambling problems and Markov decision processes. Handbook of Markov Decision Processes (2002) (Kluwer)409–428Crossref, Google Scholar
• Dunford N., Schwartz J. T.Linear Operators, Part 1: General Theory (1958) (Wiley, New York) Google Scholar
• Hinderer K. Lipschitz continuous Markov decision processes. Unpublished lecture notes. Appl. Probab. Conf. (1995) Atlanta, GAGoogle Scholar
• Klein E., Thompson A. C.Theory of Correspondences (1984) (Wiley-Interscience, New York) Google Scholar
• Langen H-J. Convergence of dynamic programming models. Math. Oper. Res. (1981) 6:493–512Link, Google Scholar
• Laraki R. On the regularity of the convexification operator on a compact set. J. Convex Anal. (2004) 11(1):209–234Google Scholar
• Maitra A. P. A note on positive dynamic programming. Ann. Math. Statist. (1969) 40:316–318Crossref, Google Scholar
• Maitra A. P., Sudderth W. D.Discrete Gambling and Stochastic Games (1996) (Springer-Verlag, New York) Crossref, Google Scholar
• Maitra A. P., Sudderth W. D. Saturations of gambling houses. Séminaire de Probabilités XXXIV (2000) (Springer-Verlag, New York) 218–238Lecture Notes in Mathematics, No. 1729Crossref, Google Scholar
• Müller A. How does the value of a Markov decision process depend on the transition probabilities? Math. Oper. Res. (1997) 22:872–885Link, Google Scholar
• Salinetti G., Wets R. On the convergence of sequences of convex sets in finite dimensions. SIAM Rev. (1979) 21:16–33Crossref, Google Scholar
• Schäl M. On stochastic dynamic programming: A bridge between Markov decision processes and gambling. Markov Processes and Control Theory, Math. Res. (1989) (Akademie-Verlag, Berlin, Germany) 178–216No. 54Google Scholar
• Sion M. On general minmax theorems. Pacific J. Math. (1958) 8:171–176Crossref, Google Scholar
• Širjaev A. N.Statistical Sequential Analysis: Optimal Stopping Rules (1973) (American Mathematical Society, Providence, RI) Translations of Mathematical MonographsGoogle Scholar