Deterministic approximations of probability inequalities

Bahadur RR, Rao R (1960) On deviations of the sample mean. Annals of Mathematical Statistics 31:1015–1027 Bennett G (1962) Probability inequalities for the sum of independent random variables. Journal of the American Statistical Association 57:33–45 Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer-Verlag, New York Chernoff H (1952) A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics 23:493–507 Dawson DA, Sankoff D (1967) An inequality for probabilities. Proceedings of the American Mathematical Society 18:504–507 Dempster MAH (1980) Introduction to stochastic programming. In: Dempster MAH (ed) Stochastic programming. Academic Press, London, pp 3–59 Dupacova J (1980) On minimax decision rules in stochastic programming. In: Prekopa A (ed) Mathematical methods of operations research, vol 1. Publishing House of the Academy of Sciences, Budapest, pp 38–48 Dupacova J (1987) The minimax approach to stochastic programming and an illustrative application. Stochastics 20:73–88 Feller W (1971) An introduction to probability theory and its applications, vol II (2nd ed). John Wiley and Sons, New York Galambos J (1977) Bonferroni inequalities. Annals of Probability 5:577–581 Godwin HJ (1955) On generalizations of Tchebychef's inequality. Journal of the American Statistical Association 50:923–945 Hoeffding W (1963) Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58:13–30 Huang C, Ziemba W, Ben-Tal A (1977) Bounds on the expectation of a convex function of a random variable: with applications to stochastic programming. Operations Research 25:315–325 Kall P, Stoyan D (1982) Solving stochastic programming problems with recourse including error bounds. Mathematische Operationsforschung und Statistik, Series Optimization 13:431–447 Kankova V (1977) Optimum solution of a stochastic optimization problem with unknown parameters. In: Transactions of the 7th Prague Conference (1974). Academia, Prague, pp 239–244 Karlin S, Studden WJ (1966) Tchebycheff systems: with applications in analysis and statistics. Interscience, New York Klein Haneveld WK (1985) Duality in stochastic linear and dynamic programming. PhD Thesis, University of Groningen Kwerel SM (1975) Most stringent bounds on aggregated probabilities of partially specified dependent probability systems. Journal of the American Statistical Association 70:472–479 Lootsma FA, Meisner J, Schellemanns F (1986) Multi-criteria decision analysis as an aid to the strategic planning of energy R&D. European Journal of Operational, Research 25:216–234 Marshall AW, Olkin I (1979) Inequalities: theory of majorization and its applications. Academic Press, New York Madansky A (1960) Inequalities for stochastic linear programming problems. Management Science 6:197–204 Móri TF, Székely GJ (1985) A note on the background of several Bonferroni-Galambos-type in-equalities. Journal of Applied Probability 22:836–843 Okamoto M (1958) Some inequalities relating to the partial sum of binomial probabilities. Annals of the Institute of Statistical Mathematics 10:29–35 Percus OE, Percus JK (1985) Probability bounds on the sum of independent nonidentically distributed binomial random variables. SIAM Journal on Applied Mathematics 45:621–640 Platz O (1985) A sharp upper probability bound for the occurence of at leastm out ofn events. Journal of Applied Probability 22:978–981 Pintér J (1985) A modified Bernstein-technique for estimating noise-perturbed function values. Calcolo 22:241–247 Prohorov YuV (1959) An extremal problem in probability theory. Theory of Probability and Its Applications 4:201–203 Sathe YS, Pradhan M, Shah SP (1980) Inequalities for the probability of the occurence of at leastm out ofn events. Journal of Applied Probability 17:1127–1132 Seppala Y (1975) On a stochastic multi-facility location problem. AIEE Transactions 7:56–62 Sinha SM (1963) Stochastic programming. PhD Thesis, University of California, Berkeley Szántai T (1985) Computing the value of multivariate probability distribution functions. PhD Thesis, Eötvös L. University, Budapest Wets R (1983) Stochastic programming: solution techniques and approximation schemes. In: Bachem A, Grötschel M, Korte B (eds) Mathematical programming: the state of the art. Springer-Verlag, Berlin Heidelberg New York, pp 566–603 Yudin DB (1980) Problems and methods of stochastic programming. Publishing House “Sovietskoye Radio”, Moscow (in Russian)