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2010 | 64 | 2 |
Tytuł artykułu

On a nonstandard approach to invariant measures for Markov operators

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Języki publikacji
We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.
Opis fizyczny
  • Albeverio, S., Fenstad, J. E., Høegh-Krohn, R. and Lindstrøm, T., Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, Orlando, 1986.
  • Anderson, R. M., Star-finite representations of measure spaces, Trans. Amer. Math. Soc. 271 (1982), 667-687.
  • Benci, V., Di Nasso, M. and Forti, M., The eightfold path to nonstandard analysis, Nonstandard Methods and Applications in Mathematics, Lecture Notes in Logic, 25, ASL, La Jolla, CA, 2006.
  • Chang, C. C., Keisler, H. J., Model Theory, 3rd edition, North-Holland, Amsterdam, 1990.
  • Di Nasso, M., On the foundations of nonstandard mathematics, Math. Japonica 50 (1999), 131-160.
  • Dudley, R. M., Real Analysis and Probability, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1989.
  • Foguel, S. R., Existence of invariant measures for Markov processes. II, Proc. Amer. Math. Soc. 17 (1966), 387-389.
  • Landers, D., Rogge, L., Universal Loeb-measurability of sets and of the standard part map with applications, Trans. Amer. Math. Soc. 304 (1987), 229-243.
  • Lasota, A., From fractals to stochastic differential equations, Chaos — The Interplay Between Stochastic and Deterministic Behaviour, Karpacz ’95, (Eds. P. Garbaczewski, M. Wolf and A. Weron), 235-255, Springer-Verlag, Berlin, 1995.
  • Lasota, A., Mackey, M. C., Chaos, Fractals and Noise, Stochastic Aspects of Dynamics, Springer-Verlag, Berlin, 1994.
  • Lasota, A., Szarek, T., Lower bound technique in the theory of a stochastic differential equation, J. Differential Equations 231 (2006), 513-533.
  • Lasota, A., Yorke, J. A., Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam. 2 (1994), 41-77.
  • Loeb, P. A., Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122.
  • Loeb, P. A., Wolff, M. (Eds.), Nonstandard Analysis for the Working Mathematician, Kluwer Academic Publishers, Dordrecht, 2000.
  • Oxtoby, J. C., Ulam, S., On the existence of a measure invariant under a transformation, Ann. Math. 40 (1939), 560-566.
  • Sims, B., Ultra-techniques in Banach Space Theory, Queen’s Papers in Pure and Applied Math., Vol. 60, Queen’s University, Kingston, Ont., 1982.
  • Stettner, Ł., Remarks on ergodic conditions for Markov processes on Polish spaces, Bull. Polish Acad. Sci. Math. 42 (1994), 103-114.
  • Szarek, T., The stability of Markov operators on Polish spaces, Studia Math. 143 (2000), 145-152.
  • Szarek, T., Invariant measures for Markov operators with application to function systems, Studia Math. 154 (2003), 207-222.
  • Szarek, T., Invariant measures for nonexpansive Markov operators on Polish spaces, Dissertationes Math. 415 (2003), 62 pp.
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