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SOME REMARKS ON BLACKWELL–ROSS MARTINGALE INEQUALITIES

Published online by Cambridge University Press:  15 December 2006

Rasul A. Khan
Rasul A. Khan
Affiliation:
Cleveland State University, Cleveland, OH, E-mail: r.khan@csuohio.edu
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Abstract

Under a suitable condition on the conditional moment generating function of the martingale differences, an exponential supermartingale is used to generalize certain martingale inequalities due to Blackwell and Ross.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 1 , January 2007 , pp. 109 - 115
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Alon, N. & Spencer, J.H. (1992). The probabilistic method. New York: Wiley.
Blackwell, D. (1954). On optimal systems. Annals of Mathematical Statistics 25: 394–397.Google Scholar
Blackwell, D. (1997). Large deviations for martingales. Festschrift for Lucien Lecam. New York: Springer, pp. 89–91.
Khan, R.A. & Tomkins, R.J. (2000). Refinements of the Dubins–Savage inequality. Journal of Theoretical Probability 13: 659–672.Google Scholar
Ross, S.M. (1995). Extending Blackwell's stengthening of Azuma's martingale inequality. Probability in the Engineering and Informational Sciences 9: 493–496.Google Scholar