Limit theory for some positive stationary processes with infinite mean

 Access to full text

1. [1] J. Aaronson. An Introduction to Infinite Ergodic Theory. Am. Math. Soc., Providence, RI, 1997. Zbl0882.28013MR1450400
2. [2] J. Aaronson. The asymptotic distributional behaviour of transformations preserving infinite measures. J. Anal. Math.39 (1981) 203–234. Zbl0499.28013MR632462
3. [3] J. Aaronson. Random $f$-expansions. Ann. Probab.14 (1986) 1037–1057. Zbl0658.60050MR841603
4. [4] J. Aaronson and M. Denker. Lower bounds for partial sums of certain positive stationary processes. In Almost Everywhere Convergence (Columbus, OH, 1988) 1–9. Academic Press, Boston, MA, 1989. Zbl0698.60023MR1035234
5. [5] J. Aaronson and M. Denker. Upper bounds for ergodic sums of infinite measure preserving transformations. Trans. Amer. Math. Soc.319 (1990) 101–138. Zbl0705.28007MR1024766
6. [6] J. Aaronson and M. Denker. On the FLIL for certain $\psi$-mixing processes and infinite measure preserving transformations. C. R. Acad. Sci. Paris Sèr. I Math.313 (1991) 471–475. Zbl0734.60033MR1127942
7. [7] J. Aaronson, M. Denker, O. Sarig and R. Zweimüller. Aperiodicity of cocycles and conditional local limit theorems. Stoch. Dyn.4 (2004) 31–62. Zbl1077.37010MR2069366
8. [8] J. Aaronson and H. Nakada. On the mixing coefficients of piecewise monotonic maps. Israel J. Math.148 (2005) 1–10. Zbl1085.37030MR2191221
9. [9] N. H. Bingham. Limit theorems for occupation times of Markov processes. Z. Wahrsch. verw. Gebiete 17 (1971) 1–22. Zbl0194.49503MR281255
10. [10] N. H. Bingham, C. M. Goldie and J. L. Teugels. Regular Variation. Cambridge Univ. Press, Cambridge, 1989. Zbl0667.26003MR1015093
11. [11] R. C. Bradley Jr.On the $\psi$-mixing condition for stationary random sequences. Trans. Amer. Math. Soc.276 (1983) 55–66. Zbl0514.60041MR684493
12. [12] R. C. Bradley Jr.Introduction to Strong Mixing Conditions 1. Kendrick Press, Heber City, UT, 2007. Zbl1133.60001
13. [13] R. A. Davis. Stable limits for partial sums of dependent random variables. Ann. Probab.11 (1983) 262–269. Zbl0511.60021MR690127
14. [14] D. A. Darling and M. Kac. On occupation times for Markoff processes. Trans. Amer. Math. Soc.84 (1957) 444–458. Zbl0078.32005MR84222
15. [15] B. I. Korenblyum. On the asymptotic behavior of Laplace integrals near the boundary of a region of convergence. Dokl. Akad. Nauk SSSR (N.S.) 104 (1955) 173–176. MR74550
16. [16] M. Rychlik. Bounded variation and invariant measures. Studia Math.76 (1983) 69–80. Zbl0575.28011MR728198
17. [17] J. D. Samur. Convergence of sums of mixing triangular arrays of random vectors with stationary rows. Ann. Probab.12 (1984) 390–426. Zbl0542.60012MR735845
18. [18] M. Thaler. Transformations on $[0,1]$ with infinite invariant measures. Israel J. Math.46 (1983) 67–96. Zbl0528.28011MR727023
19. [19] M. Thaler. The Dynkin–Lamperti arc-sine laws for measure preserving transformations. Trans. Amer. Math. Soc.350 (1998) 4593–4607. Zbl0910.28014MR1603998
20. [20] M. Thaler and R. Zweimüller. Distributional limit theorems in infinite ergodic theory. Probab. Theory Related Fields135 (2006) 15–52. Zbl1085.37005MR2214150
21. [21] M. J. Wichura. Functional laws of the iterated logarithm for the partial sums of iid random variables in the domain of attraction of a completely asymmetric stable law. Ann. Probab.2 (1974) 1108–1138. Zbl0325.60029MR358950
22. [22] R. Zweimüller. Ergodic structure and invariant densities of non-Markovian interval maps with indifferent fixed points. Nonlinearity11 (1998) 1263–1276. Zbl0922.58039MR1644385
23. [23] R. Zweimüller. Ergodic properties of infinite measure preserving interval maps with indifferent fixed points. Ergodic Theory Dynam. Sys.20 (2000) 1519–1549. Zbl0986.37008MR1786727
24. [24] R. Zweimüller. Infinite measure preserving transformations with compact first regeneration. J. Anal. Math.103 (2007) 93–131. Zbl1152.28018MR2373265
25. [25] R. Zweimüller. Measure preserving extensions and minimal wandering rates. Israel J. Math.181 (2011) 295–303. Zbl1300.37008MR2773043