On the sample path behavior of the first passage time process of a brownian motion with drift

 Access to full text

 Full (PDF)

1. A.K. Basu and M.T. Wasan, First PassageTime Process of a Standard Brownian Motion, Scand. Actuarial J., 1975, pp. 99-108. Zbl0313.60053
2. R.S. Chhikara and J.L. Folks, The Inverse Gaussian Distribution and its Statistical Application. A Review, J. R. Statist. Soc., Vol. B40, 1978, pp. 263-289. Zbl0408.62011MR522211
3. K.L. Chung and P. Erdös, On the Application of the Borel-Cantelli Lemma, Trans. Amer. Math. Soc., Vol. 72, 1952, pp. 179-186. Zbl0046.35203MR45327
4. M. Csörgó and P. Révész, How Big are the Increments of a Wiener Process?Ann. Probab., Vol. 7, 1979, pp. 731-737. Zbl0412.60038MR537218
5. M. Csörgó and P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. Zbl0539.60029MR666546
6. P. Deheuvels, L. Devroye and J. Lynch, Exact Convergence Rate in the Limit Theorems of Erdös-Rényi and Shepp, Ann. Probab., Vol. 14, 1986, pp. 209-223. Zbl0595.60033MR815966
7. P. Deheuvels and J. Steinebach, Exact Convergence Rates in Strong Approximation Laws for Large Increments of Partial Sums, Probab. Th. Rel. Fields, Vol. 76, pp. 369-393. Zbl0608.60024MR912661
8. P. Erdös and A. Rényi, On a New Law of Large Numbers, J. Analyse Math., Vol. 23, 1970, pp. 103-111. Zbl0225.60015MR272026
9. W. Feller, An Introduction to Probability Theory and Its Application, Vol. I, Wiley, New York, 3rd ed., 1978. 
10. V. Huse and J. Steinebach, On an Improved Erdös-Rényi-type Law for Increments of Partial Sums, Canad. J. Statist., Vol. 13, 1985, pp. 311-315. Zbl0588.60022MR825365
11. K. Itô and H.P. Jr. Mckean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965. Zbl0127.09503MR345224
12. N.L. Johnson and S. Kotz, Continuous Univariate Distributions-I, Wiley, New York, 1970. 
13. B. Jørgensen, Statistical Properties of the Generalized Inverse Gaussian Distributions, Lecture Notes in Statistics, Vol. 9, Springer, Berlin, 1981. Zbl0486.62022
14. J. Komlós, P. Major and G. Tusnády, An Approximation of Partial Sums of Independent r.v.'s and the Sample d.f. II., Z. Wahrsch. Verw. Geb., Vol. 34, 1976, pp. 33-58. Zbl0307.60045MR402883
15. H.R. Lerche, Boundary Crossing of Brownian Motion, Lecture Notes in Statistics, Vol. 40, Springer, Berlin, 1986. Zbl0604.62075MR861122
16. P. Lévy, Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1937. Zbl0016.17003JFM63.0490.04
17. D.M. Mason, An Extended Version of the Erdös-Rényi Strong Law of Large Numbers, Ann. Probab., Vol. 17, 1989, pp. 257-265. Zbl0677.60031MR972784
18. P. Révész, On the Increments of Wiener and Related Processes, Ann. Probab., Vol. 10, 1982, pp. 613-622. Zbl0493.60038MR659532
19. E. Schrödinger, Zur Theorie der Fall- und Steigversuche an Teilchen mit Brownscher Bewegung, Physik. Zeitschr., Vol. 16, 1915, pp. 289-295. 
20. S.J. Taylor, Regularities of Irregularities on a Brownian Path, Ann. Inst. Fourier, Grenoble, Vol. 24, 2, 1974, pp. 195-203. Zbl0262.60059MR410959
21. M.C.K. Tweedie, Statistical Properties of Inverse Gaussian Distributions I, Ann. Math. Statist., Vol. 28, 1957 a, pp. 362-377. Zbl0086.35202MR110132
22. M.C.K. Tweedie, Statistical Properties of Inverse Gaussian Distributions II, Ann. Math. Statist., Vol. 28, 1957 b, pp. 696-705. Zbl0086.35202MR110132
23. A. Wald, Sequential Analysis, Wiley, New York, 1947. Zbl0041.26303MR20764