×

zbMATH — the first resource for mathematics

The invariance principle for phi-mixing sequences. (English) Zbl 0494.60036

MSC:
60F17 Functional limit theorems; invariance principles
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Billingsley, P.: Convergence of probability measures. New York: Wiley 1968 · Zbl 0172.21201
[2] Davydov, Y.A.: Convergence of distributions generated by stationary stochastic processes. Theory Probability Appl. 8, 691–696 (1968) · Zbl 0181.44101 · doi:10.1137/1113086
[3] Durrett, R.T., Resnik, S.I.: Weak convergence with random indices. Stochastic Processes and their Appl. 5, 213–220 (1977) · Zbl 0368.60028 · doi:10.1016/0304-4149(77)90031-X
[4] Eberlein, E.: An invariance principle for lattices of dependent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 119–133 (1979) · Zbl 0397.60031 · doi:10.1007/BF00533633
[5] Ibragimov, I.A.: Some limit theorems for stationary processes. Theory Probability Appl. 7, 349–382 (1962) · Zbl 0119.14204 · doi:10.1137/1107036
[6] Ibragimov, I.A.: A note on the central limit theorem for dependent random variables. Theory Probability Appl. 20, 135–141 (1975) · Zbl 0335.60023 · doi:10.1137/1120011
[7] Ibragimov, I.A., Linnik, Yu.V.: Independent and stationary sequences of random variables. Groningen: Wolters, Noordhoff 1971 · Zbl 0219.60027
[8] Iosifescu, M., Theodorescu, R.: Random processes and learning. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0194.51101
[9] Iosifescu, M.: Limit theorems for -mixing sequences. A survey. Proceedings of the Fifth Conference on Probability Theory. Sept. 1–6 1974 Brasov, Romania, 51–57. Editura Academiei Republicii Socialiste Romania, Bucaresti 1977 · Zbl 0376.60025
[10] Lai, T.L.: Convergence rates and r-quick versions of the strong law for stationary mixing sequences. Ann. Probability 5, 693–706 (1977) · Zbl 0389.60020 · doi:10.1214/aop/1176995713
[11] McLeish, D.L.: Invariance principles for dependent variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 32, 165–178 (1975) · Zbl 0288.60034 · doi:10.1007/BF00532611
[12] Peligrad, M.: An invariance principle for dependent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 495–507 (1981) · Zbl 0485.60032 · doi:10.1007/BF01025871
[13] Philipp, W., Webb, G.R.: An invariance principle for mixing sequences of random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 25, 223–237 (1973) · Zbl 0259.60007 · doi:10.1007/BF00535894
[14] Philipp, W.: Weak and L p-invariance principles for sums of B-valued random variables. Ann. Probability 8, 68–82 (1980) · Zbl 0426.60033 · doi:10.1214/aop/1176994825
[15] Seneta, E.: Regularly varying functions. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0324.26002
[16] Serfling, R.J.: Contributions to central limit theory for dependent variables. Ann. Math. Statist. 39, 1158–1175 (1968) · Zbl 0176.48004 · doi:10.1214/aoms/1177698240
[17] Withers, C.S.: Central limit theorems for dependent variables. I. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 509–534 (1981) · Zbl 0451.60027 · doi:10.1007/BF01025872
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.