Abstract
Let (Bt,t ≥ 0) denote a real-valued Brownian motion starting from 0, and let v be a real.
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References
Bougerol, Ph. (1983). Exemples de théorèmes locaux sur les groupes résolubles. Ann. I.H.P., 19 (4), 369–391
Davis, B. (1979). Brownian motion and analytic functions. Ann. Prob., 7, 913–932
Dufresne, D. (1990). The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuarial J., 39–79
Fuchs, A. and Letta, G. (1991). Un résult at élémentaire de fiabilité. Application à la formule de Weierstrass sur la fonction gamma. Séminaire de Probabilités XXV. Lect. Notes in Maths. 1485. p. 316–323, Springer
Geman, H. and Yor, M. (October 1993). Bessel processes, Asian options and perpetuities. Mathematical Finance, 3 (4), 349–375. Paper [5] in this book
Hartman, P. (1976). Completely monotone families of solutions of n-th order linear differential equations and infinitely divisible distributions. Ann. Scuola Normale Superiore — Pisa — Classe di Scienze-Serie IV, III (2), 267–287
Itô, K. and Mc Kean, H.P. (1965). Diffusion processes and their sample paths. Springer
Kawazu, K. and Tanaka, H. (1993). On the maximum of a diffusion process in a drifted Brownian environment. Sém. Prob. XXVII, Lect. Notes in Maths. 1557, Springer, p. 78–85
Lebedev, N.N. (1972). Special functions and their applications, Dover Publications
Lévy, P. (1940). Le mouvement brownien plan. Amer. J. Math., 62, 487–550
Patterson, S.J. (1988). An introduction to the theory of the Riemann Zeta function. Cambridge Studies in Advanced Mathematics, 14
Pitman, J. and Yor, M. (1986). Level crossings of a Cauchy process. Ann. Prob., 14 (3), 780–792
Pitman, J.W. and Yor, M. (1982). A decomposition of Bessel bridges. Zeit. für Wahr., 59, 425–457
Watson, G.N. (1966). A treatise on the theory of Bessel functions. Cambridge University Press
Yor, M. (1992). Sur certaines fonctionnelles exponentielles du mouvement brownien réel. J. Appl. Proba., 29, 202–208. Paper [1] in this book
Yor, 6M. (1992). On some exponential functionals of Brownian motion. Adv. Appl. Prob., 24, 509–531. Paper [2] in this book
Yor, M. (Juin 1992). Sur les lois des fonctionnelles exponentielles du mouvement brownien, considérées en certains instants aléatoires. Note aux Comptes Rendus Acad. Sci. Paris, t. 314, Serie I, 951–956. Paper [4] in this book
Yor, M. (1992). Some aspects of Brownian motion. Part I: Some special functionals. Lectures in Mathematics. ETH Zürich. Birkhäuser
Black, F., Derman, E. and Toy, W. (January-February 1990). A one-factor model of interest rates and its application to Treasury Bond Options. Financial Analysts Journal, 33–39
Black, F. and Karasinski, P. (July-August 1991). Bond and Option pricing when short rates are lognormal. Financial Analysts Journal, 52–59
Hull, J. and White, A. (1990). Pricing interest rate derivative securities. Review of Financial Studies, 3, 573–592
Dothan, L.U. (1978). On the term structure of interest rates. Journal of Financial Economics, 6, 59–69
Gordon, L. (1994). A stochastic approach to the Gamma function. Amer. Math. Monthly, 101, 858–865
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Yor, M. (2001). Further Results on Exponential Functionals of Brownian Motion. In: Exponential Functionals of Brownian Motion and Related Processes. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56634-9_7
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