Asymptotic estimates for the first hitting time of fluctuating additive functionals of brownian motion
Séminaire de probabilités de Strasbourg, Tome 34 (2000), pp. 374-387. 
@article{SPS_2000__34__374_0,
     author = {Isozaki, Yasuki and Kotani, Shinichi},
     title = {Asymptotic estimates for the first hitting time of fluctuating additive functionals of brownian motion},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {374--387},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {34},
     year = {2000},
     mrnumber = {1768075},
     zbl = {0968.60071},
     language = {en},
     url = {http://archive.numdam.org/item/SPS_2000__34__374_0/}
}
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Isozaki, Yasuki; Kotani, Shinichi. Asymptotic estimates for the first hitting time of fluctuating additive functionals of brownian motion. Séminaire de probabilités de Strasbourg, Tome 34 (2000), pp. 374-387. http://archive.numdam.org/item/SPS_2000__34__374_0/

[1] M. Abramowitz, I.A. Stegun, A Handbook of mathematical functions, Dover, New York, 1964. | MR

[2] J. Bertoin, Lévy processes, Cambridge Univ. Press, Cambridge, 1997. | MR | Zbl

[3] Y. Isozaki, S. Watanabe, An asymptotic formula for the Kolmogorov diffusion and a refinement of Sinai's estimates for the integral of Brownian motion, Proc. Japan Acad., 70A, (1994), pp. 271-276. | MR | Zbl

[4] Y. Isozaki, Asymptotic estimates for the distribution of additive functionals of Brownian motion by the Wiener-Hopf factorization method, J. Math. Kyoto Univ., 36, (1996), pp. 211-227. | MR | Zbl

[5] A.N. Kolmogorov, Zuffälige Bewegungen, Ann. Math. II., 35 (1934), pp. 116-117. | JFM | MR | Zbl

[6] S. Kotani, S. Watanabe, Krein's spectral theory of strings and generalized diffusion processes, Functional Analysis in Markov Porcesses, ed. M. Fukushima, Lecture Notes in Mathematics 923, pp. 235-259, Springer-Verlag, Berlin, 1982. | MR | Zbl

[7] P. Mcgill, Wiener-Hopf factorization of Brownian motion, Prob. Th. Rel. Fields, 83, (1989), pp. 355-389. | MR | Zbl

[8] H.P. Mckean,Jr., A winding problem for a resonator driven by a white noise, J. Math. Kyoto Univ., 2 (1963), pp. 227-235. | MR | Zbl

[9] F. Oberhettinger, L. Badii, Tables of Laplace Transforms, Springer-Verlag, Berlin, 1973. | MR | Zbl

[10] L.C.G. Rogers, D. Williams, A differential equation in Wiener-Hopf theory, Stochastic analysis and applications, ed. A. Truman, D. Williams, Lecture Notes in Mathematics 1095, pp. 187-199, Springer-Verlag, Berlin, 1984. | MR | Zbl

[11] D. Revuz, M. Yor, Continuous martingales and Brownian motion, Springer-Verlag, Berlin, 1991. | MR | Zbl

[12] Ya.G. Sinai, Distribution of some functionals of the integral of a random walk, Theor. Math. Phys., 90 (1992), pp. 219-241. | MR | Zbl

[13] V.M. Zolotarev, Mellin-Stieltjes transforms in probability theory, Theor. Prob. Appl., 2 (1957), pp. 433-460. | MR