Project Euclid

References

• [1] L. Alili and P. Patie, Boundary-crossing identities for diffusions having the time-inversion property. J. Theoret. Probab. 23 (2010), no. 1, 65–84.
  Zentralblatt MATH: 1197.60080
  Digital Object Identifier: doi:10.1007/s10959-009-0245-3
  
• [2] J. Bertoin and M. Yor, On subordinators, self-similar Markov processes and some factorizations of the exponential variable. Electron. Comm. Probab. 6 (2001), 95–106.
  Zentralblatt MATH: 1024.60030
  Digital Object Identifier: doi:10.1214/ECP.v6-1039
  
• [3] J. Bertoin, M. Yor, Exponential functionals of Lévy processes. Probab. Surv. 2 (2005), 191–212.
  Zentralblatt MATH: 1189.60096
  Digital Object Identifier: doi:10.1214/154957805100000122
  
• [4] A.N. Borodin; P. Salminen: Handbook of Brownian motion: facts and formulae. Birkhauser, 2002.
  Zentralblatt MATH: 1012.60003
  
• [5] David, M., DeLong, Crossing probabilities for a square root boundary by a Bessel process. Comm. Statist. A–Theory Methods 10 (1981), no. 21, 2197–2213.
  Zentralblatt MATH: 0467.60070
  Digital Object Identifier: doi:10.1080/03610928108828182
  
• [6] David, M. DeLong, Erratum: "Crossing probabilities for a square root boundary by a Bessel process” [ Comm. Statist. A–Theory Methods 10 (1981), no. 21, 2197–2213; MR 82i:62119]. Comm. Statist. A–Theory Methods 12 (1983), no. 14, 1699.
  Zentralblatt MATH: 0467.60070
  Digital Object Identifier: doi:10.1080/03610928108828182
  
• [7] D. Dufresne, The distribution of a perpetuity, with applications to risk theory and pension funding, Scand. Actuarial J. No. 1–2 (1990), 39–79.
  Zentralblatt MATH: 0743.62101
  Digital Object Identifier: doi:10.1080/03461238.1990.10413872
  
• [8] N. Enriquez, C. Sabot and M. Yor, Renewal series and square-root boundary for Bessel processes, Elect. Comm. in Proba. 13 (2008), 649–652.
  Zentralblatt MATH: 1190.60031
  Digital Object Identifier: doi:10.1214/ECP.v13-1436
  
• [9] A. Göing-Jaeschke and M. Yor, A survey and some generalizations of Bessel processes, Bernoulli 9 (2003), 313–349.
• [10] Charles M. Goldie, Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1 (1991), no. 1, 126–166.
  Zentralblatt MATH: 0724.60076
  Digital Object Identifier: doi:10.1214/aoap/1177005985
  Project Euclid: euclid.aoap/1177005985
  
• [11] I.S. Gradshteyn; I.M. Ryzhik: Table of integrals, series and products. Elsevier Academic Press, Sixth Edition, 2000.
• [12] H. Kesten, Renewal theory for functionals of a Markov chain with general state space, Ann. Probab. 2 (1974), 355–386.
  Zentralblatt MATH: 0303.60090
  Digital Object Identifier: doi:10.1214/aop/1176996654
  Project Euclid: euclid.aop/1176996654
  
• [13] N.N. Lebedev, Special Functions and Their Applications, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1965. xii + 308, 1965.
• [14] H. Matsumoto and M. Yor, An analogue of Pitman’s $2M-X$ theorem for exponential Wiener functionals, Part I, a time-inversion approach, Nagoya Math. J. 159 (2000), 125–166.
• [15] P. Patie, Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 3, 667–684.
  Zentralblatt MATH: 1180.31010
  Digital Object Identifier: doi:10.1214/08-AIHP182
  Project Euclid: euclid.aihp/1249391379
  
• [16] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd. Ed., Springer, 1999.
  Zentralblatt MATH: 0917.60006
  
• [17] M. Yor, On square-root boundaries for Bessel processes, and pole-seeking Brownian motion, Stochastic analysis and applications (Swansea, 1983), 100–107, Lec. Notes Math. 1095, Springer, 1984.