Whittle type inequality for demisubmartingales

Author:
B. L. S. Prakasa Rao

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3719-3724

MSC (2000):
Primary 60E15

DOI:
https://doi.org/10.1090/S0002-9939-02-06517-6

Published electronically:
May 15, 2002

MathSciNet review:
1920053

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Abstract | References | Similar Articles | Additional Information

Abstract: A Whittle type inequality for demisubmartingales is derived and a strong law of large numbers for functions of a demisubmartingale is obtained.

**1.**Christofides, T.C.: Maximal inequalities for demimartingales and a strong law of large numbers,*Statist. Probab. Lett.*, 50 (2000), 357-363. MR**2001m:60032****2.**Dufresnoy, J.: Autour de l'inegalite de Kolmogorov,*C. R. Acad. Sci. Paris*, 264A (1967), 603. MR**37:5909****3.**Hajek, J. and Renyi, A.: A generalization of an inequality of Kolomogorov,*Acta. Math. Acad. Sci. Hung.*, 6 (1955), 281-284. MR**17:864a****4.**Newman, C.M. and Wright, A.L.: Associated random variables and martingale inequalities,*Z. Wahrsch. Verw. Geb.*, 59 (1982), 361-371. MR**85d:60088****5.**Prakasa Rao, B.L.S.: Hajek-Renyi type inequality for associated sequences,*Statist. Probab. Lett.*, 2001 (to appear).**6.**Prakasa Rao, B.L.S.: Application of Whittle's inequality for Banach space valued martingales,*Statist. Probab. Lett.*, 2001 (to appear).**7.**Prakasa Rao, B.L.S. and Dewan, I.: Associated sequences and related inference problems, In*Handbook of Statistics: Stochastic Processes: Theory and Methods*, (Edited by D.N. Shanbhag and C.R.Rao), North Holland, Amsterdam, 19 (2001), 693-728. CMP**2002:03****8.**Rao, P.: Whittle's inequality in Hilbert space,*Theory of Probability and Mathematical Statistics*, 16 (1978), 111-116. MR**55:13517****9.**Roussas, G.G.: Positive and negative dependence with some statistical applications, In*Asymptotics, Nonparametrics and Time Series*, (Edited by S.Ghosh), Marcel Dekker, New York, 1999, 757-788. CMP**2000:05****10.**Sen, P.K.: A Hajek-Renyi inequality for stochastic vectors with applications to simultaneous confidence regions,*Ann. Math. Statist.*, 42 (1971), 1132-1134.**11.**Shixin, Gan.: The Hajek-Renyi inequality for Banach space valued martingales and the smoothness of Banach spaces,*Statist. Probab. Lett.*, 32 (1997), 245-248. MR**97k:60006****12.**Whittle, P.: Refinements of Kolmogorov's inequality,*Theory Probab. Appl.*, 14 (1969), 310-311. MR**39:7657**

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Additional Information

**B. L. S. Prakasa Rao**

Affiliation:
Indian Statistical Institute, 7, SJSS Marg, New Delhi 110 016, India

Email:
blsp@isid.ac.in

DOI:
https://doi.org/10.1090/S0002-9939-02-06517-6

Keywords:
Whittle's inequality,
Kolmogorov's inequality,
maximal inequality,
Hajek-Renyi inequality,
Dufresnoy's inequality,
demisubmartingale,
demimartingale,
associated sequences,
strong law of large numbers

Received by editor(s):
June 15, 2001

Received by editor(s) in revised form:
August 3, 2001

Published electronically:
May 15, 2002

Communicated by:
Claudia M. Neuhauser

Article copyright:
© Copyright 2002
American Mathematical Society