The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. Bertoin, Jean. Lévy processes. Cambridge Tracts in Mathematics, 121. Cambridge University Press, Cambridge, 1996. x+265 pp. ISBN: 0-521-56243-0 MR1406564 (98e:60117)  
  2. Borodin, Andrei N.; Salminen, Paavo. Handbook of Brownian motion---facts and formulae. Second edition. Probability and its Applications. Birkhäuser Verlag, Basel, 2002. xvi+672 pp. ISBN: 3-7643-6705-9 MR1912205 (2003g:60001)
  3. Borodin, A. N.; Salminen, P.. On some exponential integral functionals of $rm BM(µ)$ and $rm BES(3)$. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 311 (2004), Veroyatn. i Stat. 7, 51--78, 298--299; translation in J. Math. Sci. (N. Y.) 133 (2006), no. 3, 1231--1248 MR2092200 (2005h:60246) 
  4. Breiman, Leo. Probability. Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont. 1968 ix+421 pp. MR0229267 (37 #4841)
  5. Chung, Kai Lai; Zhao, Zhong Xin. From Brownian motion to Schrödinger's equation. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 312. Springer-Verlag, Berlin, 1995. xii+287 pp. ISBN: 3-540-57030-6 MR1329992 (96f:60140) 
  6. Dellacherie, Claude; Meyer, Paul-André. Probabilités et potentiel. (French) Chapitres I à IV. Édition entièrement refondue. Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. XV. Actualités Scientifiques et Industrielles, No. 1372. Hermann, Paris, 1975. x+291 pp. MR0488194 (58 #7757) 
  7. Dufresne, Daniel. The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuar. J. 1990, no. 1-2, 39--79. MR1129194 (92i:62195)
  8. Durrett, Richard. Probability. Theory and examples. The Wadsworth & Brooks/Cole Statistics/Probability Series. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991. x+453 pp. ISBN: 0-534-13206-5 MR1068527 (91m:60002)
  9. Engelbert, H. J.; Senf, T. On functionals of a Wiener process with drift and exponential local martingales. Stochastic processes and related topics (Georgenthal, 1990), 45--58, Math. Res., 61, Akademie-Verlag, Berlin, 1991. MR1127879 (92h:60072)
  10. Erickson, K. Bruce; Maller, Ross A. Generalised Ornstein-Uhlenbeck processes and the convergence of Lévy integrals. Séminaire de Probabilités XXXVIII, 70--94, Lecture Notes in Math., 1857, Springer, Berlin, 2005. MR2126967 (2006b:60099)
  11. Itô, Kiyosi; McKean, Henry P., Jr. Diffusion processes and their sample paths. Second printing, corrected. Die Grundlehren der mathematischen Wissenschaften, Band 125. Springer-Verlag, Berlin-New York, 1974. xv+321 pp. MR0345224 (49 #9963)
  12. Jeulin, T. Sur la convergence absolue de certaines intégrales. (French) [On the absolute convergence of certain integrals] Seminar on Probability, XVI, pp. 248--256, Lecture Notes in Math., 920, Springer, Berlin-New York, 1982. MR0658688 (84i:60047)
  13. Kallenberg, Olav. Foundations of modern probability. Probability and its Applications (New York). Springer-Verlag, New York, 1997. xii+523 pp. ISBN: 0-387-94957-7 MR1464694 (99e:60001) 
  14. Khasminskii, R. Z. On positive solutions of the equation ${cal U}+Vu=0$. Theor. Probability Appl. 4 1959 309--318. MR0123373 (23 #A700)P. Tetali. Random walks and the effective resistance of networks. J. Theor. Prob. 4 (1991), 101--109. Math. Review 92c:60097
  15. Matsumoto, Hiroyuki; Yor, Marc. Exponential functionals of Brownian motion. I. Probability laws at fixed time. Probab. Surv. 2 (2005), 312--347 (electronic). MR2203675
  16. Matsumoto, Hiroyuki; Yor, Marc. Exponential functionals of Brownian motion. II. Some related diffusion processes. Probab. Surv. 2 (2005), 348--384 (electronic). MR2203676
  17. Salminen, Paavo; Yor, Marc. Perpetual integral functionals as hitting and occupation times. Electron. J. Probab. 10 (2005), no. 11, 371--419 (electronic). MR2147313 (2006a:60148)
  18. Salminen, Paavo; Yor, Marc. Properties of perpetual integral functionals of Brownian motion with drift. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 3, 335--347. MR2139023 (2006c:60096)  
  19. Simon, Barry. Functional integration and quantum physics. Pure and Applied Mathematics, 86. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. ix+296 pp. ISBN: 0-12-644250-9 MR0544188 (84m:81066)
  20. Stummer, W.; Sturm, K.-Th. On exponentials of additive functionals of Markov processes. Stochastic Process. Appl. 85 (2000), no. 1, 45--60. MR1730619 (2001b:60093)
  21. Yor, Marc. Some aspects of Brownian motion. Part I. Some special functionals. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1992. x+136 pp. ISBN: 3-7643-2807-X MR1193919 (93i:60155)

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.