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A Distribution Inequality For Martingales with Bounded Symmetric Differences

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Stochastic Processes and Related Topics

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We discuss (with some generalizations) the question of optimal strategies for the game of red-and-black with a fixed goal, with fixed subfair odds, and with both the size of legal bets allowed and the playing time limited.

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References

  1. D. L. Burkholder, Boundary value problems and sharp inequalities for martingale transforms, Ann. Probab. 12 1984, 647–702.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. L. Coolidge, The Gamblers ruin, Annals of Math. 10, 1908–1909, 181-192.

    Google Scholar 

  3. L. E. Dubins and L. J. Savage, How To Gamble If You Must: Inequalities for Stochastic Processes. McGraw-Hill, New York, 1965.

    MATH  Google Scholar 

  4. D. Heath and R. Kertz, Leaving an interval in limited playing time. Adv. Appl. Probab. 20 1988, 635–645.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Klawe, Optimal strategies for a fair betting game. Discrete Appl. Math. 1 1979, 105–115.

    Article  MathSciNet  MATH  Google Scholar 

  6. A. Maitra and W. Suddreth, Discrete Gambling and Stochastic Games. Springer, New York, 1996.

    Book  MATH  Google Scholar 

  7. D. McBeth and A. Weerasinghe, Finite-time optimal control a process leaving an interval. Jour. Appl. Probab. 33 1996, 714–728.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Yang, Optimal strategies for a betting game. Discrete Appl. Math. 28 19790, 157–169.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA, 22903, USA

    Loren D. Pitt

Authors
  1. Loren D. Pitt
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Editor information

Editors and Affiliations

  1. Departments of Mathematics & Statistics, Columbia University, New York, NY, 10027-0010, UK

    Ioannis Karatzas

  2. Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1300, USA

    Balram S. Rajput

  3. Department of Mathematics, Boston University, Boston, MA, 02215-2411, USA

    Murad S. Taqqu

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© 1998 Springer Science+Business Media New York

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Pitt, L.D. (1998). A Distribution Inequality For Martingales with Bounded Symmetric Differences. In: Karatzas, I., Rajput, B.S., Taqqu, M.S. (eds) Stochastic Processes and Related Topics. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2030-5_19

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  • DOI: https://doi.org/10.1007/978-1-4612-2030-5_19

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7389-9

  • Online ISBN: 978-1-4612-2030-5

  • eBook Packages: Springer Book Archive

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