Tightness bounds

for strongly mixing random sequences

Author:
Richard C. Bradley

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1481-1486

MSC (2000):
Primary 60G10; Secondary 60G07

DOI:
https://doi.org/10.1090/S0002-9939-99-05404-0

Published electronically:
October 5, 1999

MathSciNet review:
1676307

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Abstract | References | Similar Articles | Additional Information

Abstract: For a given strictly stationary, strongly mixing random sequence for which the distributions of the partial sums are tight, certain ``tightness bounds" exist which depend only on the marginal distribution and the mixing rate.

**[1]**R.C. Bradley,*On the dissipation of partial sums from a stationary strongly mixing sequence*, Stochastic Process. Appl.**54**(1994), 281-290. MR**95j:60054****[2]**R.C. Bradley,*On a theorem of K. Schmidt*, Statist. Probab. Letters**24**(1995), 9-12. MR**96g:60048****[3]**R.C. Bradley,*On quantiles and the central limit question for strongly mixing sequences*, J. Theor. Probab.**10**(1997), 507-555. MR**98h:60024****[4]**H. Dehling, M. Denker, and W. Philipp,*Central limit theorems for mixing sequences of random variables under minimal conditions*, Ann. Probab.**14**(1986), 1359-1370. MR**88d:60065****[5]**M. Denker,*Uniform integrability and the central limit theorem for strongly mixing processes*, Dependence in Probability and Statistics (E. Eberlein, M.S. Taqqu, eds.), pp.269-274, Birkhäuser, Boston, 1986. MR**88h:60044****[6]**N. Herrndorf,*Stationary strongly mixing sequences not satisfying the central limit theorem*, Ann. Probab.**11**(1983), 809-813. MR**84m:60030****[7]**T. Mori and K. Yoshihara,*A note on the central limit theorem for stationary strong-mixing sequences*, Yokohama Math J.**34**(1986), 143-146. MR**88g:60068****[8]**M. Rosenblatt,*A central limit theorem and a strong mixing condition*, Proc. Natl. Acad. Sci. U.S.A.**42**(1956), 43-47. MR**17:635b****[9]**K. Schmidt,*Cocyles on Ergodic Transformation Groups*, Macmillan, Delhi, 1977. MR**58:28262**

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Additional Information

**Richard C. Bradley**

Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405-5701

Email:
bradleyr@indiana.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05404-0

Keywords:
Strictly stationary,
strong mixing,
tightness

Received by editor(s):
June 25, 1998

Published electronically:
October 5, 1999

Additional Notes:
This work was partially supported by NSF grant DMS 9703712.

Communicated by:
Stanley Sawyer

Article copyright:
© Copyright 2000
American Mathematical Society