Abstract
We give a simple proof of the following result by Dufresne [Duf90]: if {w s { s ≥0 is a linear Brownian motion and c a positive constant,
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References
[Bai07] Ismaël Bailleul. Poisson boundary of a relativistic diffusion. A paraitre dans P.T.R.F., 2007.
[Bas98] Richard F. Bass. Diffusions and elliptic operators. Probability and its Applications (New York). Springer-Verlag, New York, 1998.
[Bel87] Denis R. Bell. The Malliavin calculus, volume 34 of Pitman Monographs and Surfeys in Pure and Applied Mathematics. Longman Scientific & Technical, Harlow, 1987.
[CPY01] Philippe Carmona, Frédérique Petit, and Marc Yor. Exponential functionals of Lévy processes. In Lévy processes, pages 41–55. Birkhäuser Boston, Boston, MA, 2001.
[Duf90] Daniel Dufresne. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuar. J., (1–2): 39–79, 1990.
[Mal97] Paul Malliavin. Stochastic analysis, volume 313 of Grundlehren der Mathemotischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1997.
[MY05a] Hirojuki Matsumoto and Marc Yor. Exponential functionals of Brownian motion. I. Probability laws at fixed time. Probab. Surv., 2: 312–347 (electronic), 2005.
[MY05b] Hirojuki Matsumoto and Marc Yor. Exponential functionals of Brownian motion. II. Some related diffusion processes. Probab. Surv., 2: 348–384 (electronic), 2005.
[Nua06] David Nualart. The Malliavin calculus and related topics. Probability and its Applications (New York). Springer-Verlag, Berlin, second edition, 2006.
[Yor92] Marc Yor. Sur certaines fonctionnelles du mouvement brownien réel. J. Appl. Probab., 29(1): 202–208, 1992.
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Bailleul, I. (2008). Une preuve simple d’un résultat de Dufresne. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_10
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DOI: https://doi.org/10.1007/978-3-540-77913-1_10
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