References

1. Berkes, I.; Dehling, H. Some limit theorems in log density. Ann. Probab. 21 (1993), no. 3, 1640--1670. MR1235433 (94h:60026)
2. Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871 (88i:26004)
3. Billingsley, P. . Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396 (38 #1718)
4. Bingham, N. H. Limit theorems for occupation times of Markov processes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 17 1971 1--22. MR0281255 (43 #6974)
5. Breiman, L.. On the tail behavior of sums of independent random variables. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 1967 20--25. MR0226707 (37 #2294)
6. Cs?rgő, M.; RÈvÈsz, P. Strong approximations in probability and statistics. Probability and Mathematical Statistics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. 284 pp. ISBN: 0-12-198540-7 MR0666546 (84d:60050)
7. de Acosta, A.; GinÈ, E.. Convergence of moments and related functionals in the general central limit theorem in Banach spaces. Z. Wahrsch. Verw. Gebiete 48 (1979), no. 2, 213--231. MR0534846 (80h:60011)
8. Darling, D. A.; Kac, M. On occupation times for Markoff processes. Trans. Amer. Math. Soc. 84 (1957), 444--458. MR0084222 (18,832a)
9. Durrett, R.. Probability. Theory and examples. The Wadsworth & Brooks/Cole Statistics/Probability Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991. x+453 pp. ISBN: 0-534-13206-5 MR1068527 (91m:60002)
10. Feller, W.. Fluctuation theory of recurrent events. Trans. Amer. Math. Soc. 67, (1949). 98--119. MR0032114 (11,255c)
11. Fisher, A. M.. A Pathwise Central Limit Theorem for random walks. Univ. of Goettingen preprint series, (1987); accepted for publication in the Annals of Probability (1989).
12. Fisher, A.M. . Convex-invariant means and a pathwise central limit theorem. Adv. in Math. 63 (1987), no. 3, 213--246. MR0877784 (88g:60058)
13. Fisher, A.M.; Lopes, A.; Talet, M. Self-similar returns in the transition from finite to infinite measure. In preparation.
14. Fomin, S. Finite invariant measures in the flows. (Russian) Rec. Math. [Mat. Sbornik] N. S. 12(54), (1943). 99--108. MR0009097 (5,101b)
15. Fisher, A.M.; Talet, M. Dynamical attraction to stable processes. To appear in Annales de l'Institut Henri Poincare.
16. Fisher, A.M.; Talet, M. Log averages and self-similar return sets. Submitted.
17. Horv·th, L.. Strong approximation of renewal processes. Stochastic Process. Appl. 18 (1984), no. 1, 127--138. MR0757352 (85k:60046)
18. KomlÛs, J.; Major, P.; Tusn·dy, G. An approximation of partial sums of independent RV's, and the sample DF. II. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 34 (1976), no. 1, 33--58. MR0402883 (53 #6697)
19. Major, P.. Approximation of partial sums of i.i.d.r.v.s. $i.i.d.r.v.s.$ when the summands have only two moments. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 35 (1976), no. 3, 221--229. MR0415744 (54 #3824)
20. Major, P.. The approximation of partial sums of independent RV's. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 35 (1976), no. 3, 213--220. MR0415743 (54 #3823)
21. Skorohod, A. V. Limit theorems for stochastic processes with independent increments. (Russian) Teor. Veroyatnost. i Primenen. 2 1957 145--177. MR0094842 (20 #1351)
22. Stone, C.. Weak convergence of stochastic processes defined on semi-infinite time intervals. Proc. Amer. Math. Soc. 14 1963 694--696. MR0153046 (27 #3015)
23. Strassen, V. An invariance principle for the law of the iterated logarithm. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 1964 211--226 (1964). MR0175194 (30 #5379)
24. Strassen, V.. Almost sure behavior of sums of independent random variables and martingales. 1967 Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Vol. II: Contributions to Probability Theory, Part 1, pp. 315--343 Univ. California Press, Berkeley, Calif. MR0214118 (35 #4969)
25. Vervaat, W.. Functional central limit theorems for processes with positive drift and their inverses. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 23 (1972), 245--253. MR0321164 (47 #9697)
26. Walters, P.. An introduction to ergodic theory. Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. ISBN: 0-387-90599-5 MR0648108 (84e:28017)
27. Whitt, W.. Some useful functions for functional limit theorems. Math. Oper. Res. 5 (1980), no. 1, 67--85. MR0561155 (81e:60035)
28. Whitt, W.. Stochastic-process limits. An introduction to stochastic-process limits and their application to queues. Springer Series in Operations Research. Springer-Verlag, New York, 2002. xxiv+602 pp. ISBN: 0-387-95358-2 MR1876437 (2003f:60005)