## Rocky Mountain Journal of Mathematics

### A Restricted Dichotomy of Equivalence Classes for Some Measures of Dependence

#### Article information

Source
Rocky Mountain J. Math., Volume 31, Number 3 (2001), 831-872.

Dates
First available in Project Euclid: 5 June 2007

https://projecteuclid.org/euclid.rmjm/1181070177

Digital Object Identifier
doi:10.1216/rmjm/1020171670

Mathematical Reviews number (MathSciNet)
MR1877325

Zentralblatt MATH identifier
1001.60040

#### Citation

Bradley, Richard C. A Restricted Dichotomy of Equivalence Classes for Some Measures of Dependence. Rocky Mountain J. Math. 31 (2001), no. 3, 831--872. doi:10.1216/rmjm/1020171670. https://projecteuclid.org/euclid.rmjm/1181070177

#### References

• C. Bennett and R. Sharpley, Interpolation of operators, Academic Press, Boston, 1988.
• J. Bergh and J. Löfström, Interpolation spaces, Springer-Verlag, New York, 1976.
• R.C. Bradley, On tightness of partial sums from strictly stationary, absolutely regular sequences of $B$-valued random variables, J. Math. Anal. Appl. 240 (1999), 128-144.
• R.C. Bradley and W. Bryc, Multilinear forms and measures of dependence between random variables, J. Multivariate Anal. 16 (1985), 335-367.
• R.C. Bradley, W. Bryc and S. Janson, On dominations between measures of dependence, J. Multivariate Anal. 23 (1987), 312-329.
• --------, Remarks on the foundations of measures of dependence, in New perspectives in theoretical and applied statistics (M.L. Puri, J.P. Vilaplana and W. Wertz, eds.), Wiley, New York, 1987, pp. 421-437.
• H. Dehling and W. Philipp, Almost sure invariance principles for weakly dependent vector-valued random variables, Ann. Probab. 10 (1982), 689-701.
• P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Statist. 30 (1994), 63-82.
• I.A. Ibragimov and Yu.V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff, Groningen, 1971.
• F. Merlevède, M. Peligrad and S.A. Utev, Sharp conditions for the CLT of linear processes in a Hilbert space, J. Theoret. Probab. 10 (1997), 681-693.
• W. Philipp, Weak and $L^p$-invariance principles for sums of $B$-valued random variables, Ann. Probab. 8 (1980), 68-82, (correction ibid. 14 (1986), 1095-1101).
• M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 43-47.
• --------, Markov processes, structure and asymptotic behavior, Springer-Verlag, Berlin, 1971.
• P. Shields, The theory of Bernoulli shifts, University of Chicago Press, Chicago, 1973.
• V.A. Volkonskii and Yu.A. Rozanov, Some limit theorems for random functions, I, Theory Probab. Appl. 4 (1959), 178-197.