no. 3
Sur le premier instant de passage de l'intégrale du mouvement brownien
Annales de l'I.H.P. Probabilités et statistiques, Tome 27 (1991) no. 3, pp. 385-405 
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     author = {Lachal, A.},
     title = {Sur le premier instant de passage de l'int\'egrale du mouvement brownien},
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     pages = {385--405},
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     url = {https://www.numdam.org/item/AIHPB_1991__27_3_385_0/}
}
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Lachal, A. Sur le premier instant de passage de l'intégrale du mouvement brownien. Annales de l'I.H.P. Probabilités et statistiques, Tome 27 (1991) no. 3, pp. 385-405. https://www.numdam.org/item/AIHPB_1991__27_3_385_0/

[1] M. Abramowitz et I.A. Stegun, Handbook of Mathematical Functions with Formulas. Graphs, and Mathematical tables, Wiley, New York, 1972. | Zbl | MR

[2] Ph. Biane et M. Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sc. Math., 2e série, t. 111, 1987, p. 23-101. | Zbl | MR

[3] K.L. Chung, Lectures from Markov Processes to Brownian Motion, Springer Verlag, Berlin, 1982. | Zbl | MR

[4] D.R. Cox et H.D. Miller, The theory of Stochastic Processes, Methuen, London, 1965. | Zbl | MR

[5] E.B. Dynkin, Markov Processes, vol. 2, Springer Verlag, Berlin, 1965.

[6] A. Erdelyi, Tables of Intergral Transforms, vol. 1 and 2, McGraw-Hill, New York, 1954. | Zbl

[7] A. Friedman, Stochastic Differential Equations and Applications, vol. 2, Academic Press, New York, 1976. | Zbl | MR

[8] J. Gani et D.R. Mcneil, Joint Distributions of Random Variables and their integrals for Certain Birth-Death and Diffusion Processes, Adv. Appl. Prob. vol. 3, 1971, p. 339-352. | Zbl | MR

[9] M. Goldman, On the First Passage of the Integrated Wiener Process, Ann. Math. Stat., vol. 42, 1971, p. 2150-2155. | Zbl | MR

[10] Ju P. Gor'Kov, A Formula for the Solution of a Certain Boundary Value Problem for the Stationary Equation of Brownian Motion, Soviet. Math. Dokl. vol. 16, 1975, p. 904-908. | Zbl | MR

[11] P. Groenenboom, Brownian Motion with a Parabolic Drift and Airy Functions, Prob. Theor. Rel. Fields, vol. 81, 1989, p. 79-109.

[12] M. Kac, On the Average of a Certain Wiener Functional and a Related Limit Theorem in Calculus of Probability, Trans. Am. Math. Sec., vol. 59, 1946, p. 401-414. | Zbl | MR

[13] M. Kac, On the Distributions of Certain Wiener Functional, Trans. Am. Math. Soc., vol. 65, 1949, p. 1-13. | Zbl | MR

[14] M. Kac, Probability Theory: its Role and its Impact, S.I.A.M. Rev., vol. 4, 1962, p. 1-11. | MR

[15] M. Lefebvre, First Passage Densities of a Two-Dimensional Process, S.I.A.M. J. Appl. Math., vol. 49, 1989, p. 1514-1523. | Zbl | MR

[16] M. Lefebvre et E. Leonard, On the First Hitting Place of the Integrated Wiener Process, Adv. Appl. Prob., vol. 21, 1989, p. 945-948. | Zbl | MR

[17] P. Mcgill, Some Eigenvalue Identities for Brownian Motion, Math. Proc. Camb. Phil. Soc., vol. 105, 1989, p. 589-596. | Zbl | MR

[18] P. Mcgill, Wiener-Hopf Factorisation of Brownian Motion, Prob. Theor. Fields, vol. 83, 1989, p. 355-389. | Zbl | MR

[19] H.P.Jr. Mckean, A Winding Problem for a Resonator Driven by a White Noise, J. Math. Kyoto Univ. vol. 2, 1963, p. 227-235. | Zbl | MR

[20] J. Potter, Somme Statistical Properties of the Motion of an Oscillator Driven by a White Noise, M.I. T. doctoral dissertation.

[21] P.S. Puri, On the Homogeneous Birth-and-Death Process and Its Integral, Biometrika, vol. 53, 1966, p. 61-71. | Zbl | MR

[22] P.S. Puri, A Class of Stochastic Models of Response to Injection of Virulent bacteria in the Absence of Defense Mechanism, Fifth Berk. Symp. Math. Stat. Prob., vol. IV, 1967, p. 511-535.

[23] S.O. Rice, Mathematical Analysis of Random Noise, Bell System Techn. J., vol. 23, 1944, p. 282-332; 24, 1945, p. 46-156. | Zbl | MR

[24] L.A. Shepp, On the Integral of the Absolute Value of the Pinned Wiener Process, Ann Prob., vol. 10, 1982, p. 234-239. | Zbl | MR