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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Kulldorff, Martin 1993. Optimal Control of Favorable Games with a Time Limit. SIAM Journal on Control and Optimization, Vol. 31, Issue. 1, p. 52.
    Phatarfod, R.M. 1977. Some aspects of stochastic reservoir theory — A reply. Journal of Hydrology, Vol. 33, Issue. 1-2, p. 195.
    Collings, P. S. 1975. Dams with autoregressive inputs. Journal of Applied Probability, Vol. 12, Issue. 03, p. 533.
    Ott, T. J. 1974. Infinite divisibility and stability of finite semi-Markov matrices. Advances in Applied Probability, Vol. 6, Issue. 02, p. 217.
    Turnbull, Bruce W. 1974. An inequality for the total now in a dam with non-Markovian inputs. Advances in Applied Probability, Vol. 6, Issue. 02, p. 218.
    Ott, T. J. 1974. Infinite divisibility and stability of finite semi-Markov matrices. Advances in Applied Probability, Vol. 6, Issue. 02, p. 217.
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Chebyshev-like inequalities for dam models

  • Bruce W. Turnbull (a1)
Abstract

A dam model is proposed for which it is assumed that the conditional distributions of the inputs, given the past, are known only to lie in some class M . For selected M , bounds are derived on various quantities of interest such as the mean time to first emptiness. The case of normal inputs is treated in greater detail and a release rule is discussed. The techniques used are similar to those used in the theory of gambling as developed by Dubins and Savage (1965).

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COPYRIGHT: © Applied Probability Trust 1972 
Corresponding author
* Now at Stanford University.
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This work forms part of the author's doctoral dissertation submitted in the Department of Operations Research, Cornell University. Research supported in part by the National Science Foundation under Grant GK–21460 and by the U.S. Army Research Office under Grant DA–31–124–ARO–D–474.

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References
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Blackwell, D. (1954) On optimal systems. Ann. Math. Statist. 25, 394–397.
Blackwell, D. (1964) Probability bounds via dynamic programming. Proc. Symp. Appl. Math. 16, 277–280. Amer. Math. Soc., Providence, R. I.
Borch, K. (1967) The theory of risk. J. R. Statist. Soc. B 29, 432–452.
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Wiley, New York.
De Finetti, B. (1957) Su una impostazione alternativa della theoria collettiva del rischio. Trans. XV Int. Congr. Actuaries II, 433–443.
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.
Dubins, L. E. and Savage, L. J. (1965) How to Gamble if You Must. McGraw-Hill, New York.
Gani, J. (1969) Recent advances in storage and flooding theory. Adv. Appl. Prob. 1, 90–110.
Moran, P. A. P. (1954) A probability theory of dams and storage systems. Aust. J. Appl. Sci. 5, 116–124.
Neveu, J. (1965) Mathematical Foundations of the Calculus of Probability. Holden Day, San Francisco.
Prabhu, N. U. (1964) Time dependent results in storage theory. J. Appl. Prob. 1, 1–46.
Turnbull, B. W. (1971) Bounds and Optimal Strategies for Stochastic Systems. Ph.D. dissertation, Cornell University.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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