Bañuelos, R. and Moore, C. N. (1999). Probabilistic Behavior of Harmonic Functions. Birkhaüser, Boston. MR1707297

   Barlow, M. T. Jacka, S. D. and Yor, M. (1986). Inequalites for a pair of processes stopped at a random time. Proc. London Math. Soc. 53 142–172. MR0812449

   Bentkus, V., Bloznelis, M. and Götze, F. (1996). A Berry-Essen bound for Student’s statistic in the non i.i.d. case. J. Theoret. Probab. 9 765–796. MR1400598

   Bentkus, V. and Götze, F. (1996). The Berry-Esseen bound for Student’s statistic. Ann. Probab. 24 491–503. MR1387647

   Bercu, B. (2001). On large deviations in the Gaussian autoregressive process: stable, unstable and explosive cases. Bernoulli 7 299–316. MR1828507

   Bercu, B., Gassiat, E. and Rio, E. (2002). Concentration inequalities, large and moderate deviations for self-normalized empirical processes. Ann. Probab. 30 1576–1604. MR1944001

   Caballero, M. E., Fernández, B. and Nualart, D. (1998). Estimation of densities and applications. J. Theoret. Probab. 11 831–851. MR1633411

   Chan, H. P. and Lai, T. L. (2000). Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families. Ann. Statist. 28 1638–1669. MR1835035

   Chen, X. (1999). The law of the iterated logarithm for functionals of Harris recurrent Markov chains: Self normalization. J. Theoret. Probab. 12 421–445. MR1684752

   Chistyakov, G. P. and Götze, F. (2004). Limit distributions of Studentized means. Ann. Probab. 32 28–77. MR2040775

   de la Peña, V. H. (1999). A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 537–564. MR1681153

   de la Peña and Giné (1999). Decoupling: From Dependence to Independence. Springer, New York. MR1666908

   de la Peña, V. H., Klass, M. J. and Lai, T. L. (2000). Moment bounds for self-normalized martingales. In High Dimensional Probability II (E. Giné, D. M. Mason and J. A. Wellner, eds.) 1–11. Birkhauser, Boston. MR1857343

   Dembo, A. (1996). Moderate deviations for martingales with bounded jumps. Elect. Comm. in Probab. 1, 11–17. MR1386290

   Efron, B. and Tibshirani, R. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York. MR1270903

   Egorov, V. (1998). On the growth rate of moments of random sums. Preprint.

   Einmahl, U. and Mason, D. (1989). Some results on the almost sure behavior of martingales. In Limit Theorems in Probability and Statistics (I. Berkes, E. Csáki and P. Révész, eds.) 185–195. North-Holland, Amsterdam. MR1116787

   Erds, P. (1942). On the law of the iterated logarithm. Ann. Math. 43 419–436. MR0006630

   Giné, E. Göetze, F. and Mason, D. (1997). When is the Student t-statistic asymptotically standard normal? Ann. Probab. 25 1514–1531. MR1457629

   Giné, E. and Mason, D. M. (1998). On the LIL for self-normalized sums of i.i.d. random variables. J. Theoret. Probab. 11 (2) 351–370. MR1622575

   Graversen, S. E. and Peskir, G. (2000). Maximal inequalities for the ornstein-Uhlenbeck process. Proc. Amer. Math. Soc. 128 (10), 3035–3041. MR1664394

   Griffin, P. and Kuelbs, J. (1989). Self-normalized laws of the iterated logarithm. Ann. Probab. 17 1571–1601. MR1048947

   Griffin, P. and Kuelbs, J. (1991). Some extensions of the LIL via self-normalization. Ann. Probab. 19 380–395. MR1085343

   Jing, B. Y., Shao, Q. M. and Wang, Q. (2003). Self-normalized Cramér-type large deviations for independent random variables. Ann. Probab. 31 2167–2215. MR2016616

   Jing, B. Y., Shao, Q. M. and Zhou, W. (2004). Saddlepoint approximations for Student’s t-statistic with no moment conditions. Ann. Statist. 32 2679–2711. MR2153999

   Karatzas, I. and Shreve, S. E. (1991). Brownian Motion and Stochastic Calculus, 2nd edition. Springer, New York. MR1121940

   Khoshnevisan, D. (1996). Deviation inequalities for continuous martingales. Stoch. Process. Appl. 65 17–30. MR1422877

   Lai, T. L. (1976). Boundary crossing probabilities for sample sums and confidence sequences. Ann. Probab. 4 299–312. MR0405578

   Lai, T.L. (2004). Likelihood ratio identities and their applications to sequential analysis (with Discussion). Sequential Anal. 23 467–556. MR2103908

   Lipster, R. and Spokoiny, V. (2000). Deviation probability bound for martingales with applications to statistical estimation. Statistics and Probability Letters 46, 347–357. MR1743992

   Logan, B. F., Mallows, C. L., Rice, S. O. and Shepp, L. A. (1973). Limit distributions of self-normalized sums. Ann. Probab. 1 788–809. MR0362449

   Revuz, D. and Yor, M. (1999). Continuous Martingales and Brownian Motion, 3rd edition. Springer, New York. MR1725357

   Robbins, H. (1970). Statistical methods related to the law of the iterated logarithm. Ann. Math. Statist. 41 1379–1409. MR0277063

   Robbins, H. and Siegmund, D. (1970). Boundary crossing probabilities for the Wiener process and sample sums. Ann. Math. Statist. 41 1410–1429. MR0277059

   Shao, Q. (1997). Self-normalized large deviations. Ann. Probab. 25 285–328. MR1428510

   Shao, Q. (1999). Cramér-type large deviation for Student’s t-statistic. J. Theoret. Probab. 12 387–398.

   Stout, W. F. (1970). A martingale analogue of Kolmogorov’s law of the iterated logarithm. Z. Wahrsch. verw. Geb. 15 279–290. MR0293701

   Stout, W. F. (1973). Maximal inequalities and the law of the iterated logarithm. Ann. Probab. 1 322–328. MR0353428

   Wang, Q. and Jing, B. Y. (1999). An exponential non-uniform Berry-Essen bound for self-normalized sums. Ann. Probab. 27 2068–2088. MR1742902

   Worms, J. (2000). Principes de déviations modérées pour des martingales autonormalizées. C. R. Acad. Sci. Paris 330, Serie I, 909–914. MR1771957