On the sample path behavior of the first passage time process of a brownian motion with drift
Annales de l'I.H.P. Probabilités et statistiques, Volume 26 (1990) no. 1, pp. 145-179.
@article{AIHPB_1990__26_1_145_0,
     author = {Deheuvels, Paul and Steinebach, Josef},
     title = {On the sample path behavior of the first passage time process of a brownian motion with drift},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {145--179},
     publisher = {Gauthier-Villars},
     volume = {26},
     number = {1},
     year = {1990},
     zbl = {0699.60018},
     mrnumber = {1075443},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1990__26_1_145_0/}
}
TY  - JOUR
AU  - Deheuvels, Paul
AU  - Steinebach, Josef
TI  - On the sample path behavior of the first passage time process of a brownian motion with drift
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1990
DA  - 1990///
SP  - 145
EP  - 179
VL  - 26
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1990__26_1_145_0/
UR  - https://zbmath.org/?q=an%3A0699.60018
UR  - https://www.ams.org/mathscinet-getitem?mr=1075443
LA  - en
ID  - AIHPB_1990__26_1_145_0
ER  - 
%0 Journal Article
%A Deheuvels, Paul
%A Steinebach, Josef
%T On the sample path behavior of the first passage time process of a brownian motion with drift
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1990
%P 145-179
%V 26
%N 1
%I Gauthier-Villars
%G en
%F AIHPB_1990__26_1_145_0
Deheuvels, Paul; Steinebach, Josef. On the sample path behavior of the first passage time process of a brownian motion with drift. Annales de l'I.H.P. Probabilités et statistiques, Volume 26 (1990) no. 1, pp. 145-179. http://www.numdam.org/item/AIHPB_1990__26_1_145_0/

A.K. Basu and M.T. Wasan, First Passage Time Process of a Standard Brownian Motion, Scand. Actuarial J., 1975, pp. 99-108. | Zbl

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. | MR | Zbl

K.L. Chung and P. Erdös, On the Application of the Borel-Cantelli Lemma, Trans. Amer. Math. Soc., Vol. 72, 1952, pp. 179-186. | MR | Zbl

M. Csörgó and P. Révész, How Big are the Increments of a Wiener Process? Ann. Probab., Vol. 7, 1979, pp. 731-737. | MR | Zbl

M. Csörgó and P. Révész, Strong Approximations in Probability and Statistics, Academic Press, New York, 1981. | MR | Zbl

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. | MR | Zbl

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. | MR | Zbl

P. Erdös and A. Rényi, On a New Law of Large Numbers, J. Analyse Math., Vol. 23, 1970, pp. 103-111. | MR | Zbl

W. Feller, An Introduction to Probability Theory and Its Application, Vol. I, Wiley, New York, 3rd ed., 1978.

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. | MR | Zbl

K. Itô and H.P. Jr. Mckean, Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965. | MR | Zbl

N.L. Johnson and S. Kotz, Continuous Univariate Distributions-I, Wiley, New York, 1970.

B. Jørgensen, Statistical Properties of the Generalized Inverse Gaussian Distributions, Lecture Notes in Statistics, Vol. 9, Springer, Berlin, 1981. | Zbl

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. | MR | Zbl

H.R. Lerche, Boundary Crossing of Brownian Motion, Lecture Notes in Statistics, Vol. 40, Springer, Berlin, 1986. | MR | Zbl

P. Lévy, Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1937. | JFM | Zbl

D.M. Mason, An Extended Version of the Erdös-Rényi Strong Law of Large Numbers, Ann. Probab., Vol. 17, 1989, pp. 257-265. | MR | Zbl

P. Révész, On the Increments of Wiener and Related Processes, Ann. Probab., Vol. 10, 1982, pp. 613-622. | MR | Zbl

E. Schrödinger, Zur Theorie der Fall- und Steigversuche an Teilchen mit Brownscher Bewegung, Physik. Zeitschr., Vol. 16, 1915, pp. 289-295.

S.J. Taylor, Regularities of Irregularities on a Brownian Path, Ann. Inst. Fourier, Grenoble, Vol. 24, 2, 1974, pp. 195-203. | Numdam | MR | Zbl

M.C.K. Tweedie, Statistical Properties of Inverse Gaussian Distributions I, Ann. Math. Statist., Vol. 28, 1957 a, pp. 362-377. | MR | Zbl

M.C.K. Tweedie, Statistical Properties of Inverse Gaussian Distributions II, Ann. Math. Statist., Vol. 28, 1957 b, pp. 696-705. | MR | Zbl

A. Wald, Sequential Analysis, Wiley, New York, 1947. | MR | Zbl