Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 4 (1999) > Paper 13 open journal systems 


Convergence of Stopped Sums of Weakly Dependent Random Variables

Magda Peligrad, University of Cincinnati


Abstract
In this paper we investigate stopped partial sums for weak dependent sequences.
In particular, the results are used to obtain new maximal inequalities
for strongly mixing sequences and related almost sure results.


Full text: PDF

Pages: 1-13

Published on: April 6, 1999
Bibliography
  1. Austin, D.G., Edgar, G.A. and Ionescu Tulcea, A., (1974). Pointwise convergence in terms of expectations. Z. Wahrsch. verv Gebiete 30, 17-26. Math. Review 50 #11402.
  2. Berbee, H.C.P. (1979). Random Walks with Stationary Increments and Renewal Theory, Mathematisch Centrum, Amsterdam. Math. Review 81e:60093 .
  3. Billingsley, P. (1968). Convergence of Probability Measures, Wiley. Math. Review 38 #1718.
  4. Bradley, R.C. (1986). Basic properties of strong mixing conditions, Progress in Prob. and Stat., Dependence in Prob. and Stat., 11, E. Eberlein and M. Taqqu (eds.), 165-192. Math. Review 88g:60039.
  5. Bradley, R.C., Utev, S.A. (1994). On second order properties of mixing sequences of random fields, Prob. Theory and Math. Stat., B. Grigelionis et al (eds.), 99-120, VSP/TEV. Math. Review 99f:60092.
  6. Doukhan, P. (1994). Mixing properties and examples, Lecture Notes in Statistics 85, Springer Verlag. Math. Review 96b:60090.
  7. Edgar, G.A. and Sucheston, L. (1976). Amarts: A class of asymptotic martingales, J. Multiv. Anal., 6, 193-221. Math. Review 54 #1368.
  8. Edgar, G.A., Sucheston, L. (1992). Stopping times and directed processes, Encyclopedia of Mathematics and its Applications, Cambridge University Press. Math. Review 94a:60064.
  9. Garsia, A. (1973). On a convex function inequality for submartingales, Ann. Probab., 1, 171-174. Math. Review 49 #11618.
  10. Gut, A., Schmidt, K. (1983). Amarts and set function processes, Lecture Notes in Math 1042, Springer-Verlag. Math. Review 85k:60064.
  11. Gut, A. (1986). Stopped Random Walks Limit Theorems and Applications, Applied Probability, Springer-Verlag. Math. Review 88m:60085.
  12. Houdre, C. (1995). On the almost sure convergence of series of stationary and related nonstationary variables, Ann. Probab., 23, 1204-1218. Math. Review 96e:60051 .
  13. Ibragimov, I.A., Linnik, Yu. V. (1971). Independent and stationary sequences of random variables, Walters-Noordhoff, Groningen, the Netherlands. Math. Review 48 #1287.
  14. Krengel, V., Sucheston, L. (1978). On semiamarts, amarts and processes with finite value, Advances in Prob., 4, 197-266. Math. Review 80g:60053.
  15. McLeish, D.L. (1975). A maximal inequality and dependent strong laws. Ann. Probab., 3, 829-39. Math. Review 53 #4216.
  16. Moricz, F. (1976). Moment inequalities and strong laws of large numbers, Z. Wahrsch. Verw. Gebiete, 35, 299-314. Math. Review 53 #11717.
  17. Newman, C., Wright, A. (1982). Associated random variables and martingale inequalities, Z. Wahr. verw. Gebiete, 59, 361-371. Math. Review 85d:60088.
  18. Peligrad, M. (1985a). An invariance principle for j-mixing sequences, Ann. Probab., 13, 1304-1313. Math. Review 87b:60056.
  19. Peligrad, M. (1985b). Convergence rates of the strong law for stationary mixing sequences. Z. Wahrsch. verw. Gebiete, 70, 307-314. Math. Review 86k:60052.
  20. Peligrad, M. (1992). On the central limit theorem for weakly dependent sequences with a decomposed strong mixing coefficient. Stochastic Proc. Appl., 42, 181-193. Math. Review 93j:60044.
  21. Petrov, V.V. (1975). Sums of independent random variables, Springer Verlag. Math. Review 52 #9335.
  22. Rio, E. (1993). Covariance inequalities for strongly mixing processes, Ann. Inst. H. Poincaré, 29, 4, 589-597. Math. Review 94j:60045.
  23. Rio, E. (1995). A maximal inequality and dependent Marcinkiewicz-Zygmund strong laws, Ann. Probab. 23, 918-937. Math. Review 96e:60053.
  24. Roussas, G.G. (1991). Recursive estimation of the transition distribution function of a Markov process: asymptotic normality, Statist. Probab. Lett., 11, 435-447. Math. Review 92h:62142.
  25. Roussas, G.G. (1992). Exact rates of almost sure convergence of a recursive kernel estimate of a probability density function: application to regression and hazard rate estimation. J. Nonpar. Statist., 1, 171-195. Math. Review 94j:62091
  26. Shao, Q. (1995). Maximal inequalities for partial sums of r-mixing sequences. Ann. Probab., 23, 948-965. Math. Review 96d:60027.
  27. Shao, Q. (1993). Complete convergence for a-mixing sequences, Stat. and Prob. Letters 16, 279-287. Math. Review 94d:60036.
  28. Utev, S.A. (1991). Sums of random variables with j-mixing, Siberian Adv. Math. 1, 124-155. Math. Review CMP 1 128 381.
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489