References
P. Billingsley,Convergence of Probability Measures. Wiley (New York, 1968).
D. C. Farden, Stochastic Approximation with Correlated Data. ONR Technical Report No. 11, Department of Electrical Engineering, Colorado State University, (Fort Collins, Colorado, 1975).
M. Klass, On stopping rules and the expected supremum ofS n /a n and |S n |/a n ,Ann. Prob. 2 (1974), 889–905.
M. Longnecker andR. J. Serfling, On Almost Sure Convergence of Infinite Series. FSU Statistics Report M346 (ONR Technical Report No. 97), Florida State University (Tallahassee, Florida, 1975).
M. Longnecker andR. J. Serfling, A Note on Application of a Lemma of Billingsley FSU Statistics Report M371 (ONR Technical Report No. 103), Florida State University (Tallahassee, Florida, 1976).
P. Révész,The Laws of Large Numbers. Academic Press (New York, 1968).
R. J. Serfling, Moment inequalities for the maximum cumulative sum,Ann. Math. Statist.,41 (1970), 1227–1234.
R. J. Serfling, Convergence properties ofS n under moment restrictions,Ann. Math. Statist.,41 (1970), 1235–1248.
Author information
Authors and Affiliations
Additional information
Research supported by the Army, Navy and Air Force under Office of Naval Research Contract No. N00014-76-C-0608.
Rights and permissions
About this article
Cite this article
Longnecker, M., Serfling, R.J. General moment and probability inequalities for the maximum partial sum. Acta Mathematica Academiae Scientiarum Hungaricae 30, 129–133 (1977). https://doi.org/10.1007/BF01895656
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01895656