Abstract
The classical čebyšev inequality leads to an inequality for martingales which is often called the Kolmogorov inequality. It is shown here that many generalized čebyšev inequalities for random variables lead in a similar way to martingale inequalities, and that the corresponding martingale inequality is sharp when the čebyšev inequality is.
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Dubins, L.E., Savage, L.J.: How to gamble If You Must. New York: Dover 1965
Karlin, S.J., Studden, W.J.: čebyšeff systems: with applications in analysis and statistics. New York: Interscience 1966
Meyer, P.A.: Probability and potentials. Waltham, Mass.: Blaisdell 1966
Renyi, A.: Foundations of probability. San Francisco: Holden-Day 1970
Sudderth, W. D.: A “Fatou equation” for randomly stopped variables. Ann. Math. Statist. 42, 2143–2146 (1971)
Sudderth, W.: On measurable gambling problems. Ann. Math. Statist. 42, 260–269 (1971)
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On leave from Tel-Aviv University. Presently at the University of California, Berkeley.
Research supported by National Science Foundation Grant MPS75-06173
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Gilat, D., Sudderth, W.D. Generalized kolmogorov inequalities for martingales. Z. Wahrscheinlichkeitstheorie verw Gebiete 36, 67–73 (1976). https://doi.org/10.1007/BF00533209
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DOI: https://doi.org/10.1007/BF00533209