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 Electronic Communications in Probability > Vol. 7 (2002) > Paper 4 open journal systems 


Further Exponential Generalization of Pitman's 2M-X Theorem

Fabrice Baudoin, Université Paris 6 et Paris 7


Abstract
We present a class of processes which enjoy an exponential analogue of Pitman's 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.


Full text: PDF

Pages: 37-46

Published on: January 11, 2002
Bibliography
  1. O. Barndorff-Nielsen (1978), Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat. 5, 151-157. Math. Review 80a:60016
  2. F. Baudoin (2001), Conditionings on the Wiener space: Theory, Examples and Apllication to Finance To appear in Stochastic processes and their Applications. Math. Review number not available
  3. F. Baudoin (2001), Bessel process with random drift and the /X transformation. Preprint, Math. Review number not available
  4. J.M.C. Clark (1970), The representation of functionals of Brownian motion by stochastics integrals. Ann. Math. Stat. 41,1282-1295. Math. Review 42#5336
  5. D. Dufresne (2001), An affine property of the reciprocal Asian option process. Osaka J. Math. 38,379-381. CMP 1833627
  6. C. Donati-Martin, H. Matsumoto, M. Yor (2001), Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions. Publ. RIMS Kyoto 37,295-326. CMP 1855425
  7. N. N. Lebedev (1972), Special Functions and their Applications. Dover New-York Math. Review 50#2568
  8. H. Matsumoto and M. Yor (1999), A version of Pitman's 2M-X theorem for geometric Brownian motions. C.R. Acad. Sci. Paris 328, Série I, 1067-1074. Math. Review 2000d:60134
  9. H. Matsumoto and M. Yor (2001), A relations hip between Brownian motions with Opposite drifts via Certain Ennlargements of the Brownian filtration. Osaka J. Math 38, 383-398. CMP 1833628
  10. H. Matsumoto and M. Yor (2000), An analogue of Pitman's 2M-X theorem for Exponential Wiener functionals, Part I: A time-inversion approach. Nagoya J. Math 159, 125-166. Math. Review 2001j:60145
  11. H. Matsumoto and M. Yor (2001), An analogue of Pitman's 2M-X theorem for Exponential Wiener functionals, Part II: The role of the generalized inverse Gaussian laws. Nagoya J. Math 162, 65-86. CMP 1836133
  12. H. Matsumoto and M. Yor (1999), Some changes of probabilities related to a geometric Brownian motion version of Pitman's 2M-X theorem. Elect. Comm. in Prob. 4, 15-23. Math. Review 2000e:60130
  13. P.A. Meyer (1994), Sur une transformation du mouvement brownien due à Jeulin et Yor. Sem. Prob. XXVIII, Springer LNM 1583, 98-101. Math. Review 96b:60215
  14. J.W. Pitman and M. Yor (1980), Processus de Bessel, et mouvement brownien, avec drift. C.R. Acad. Sci. Paris Serie I 291, 151-153. Math. Review 82b:60105
  15. J.W. Pitman and M. Yor (1981), Bessel process and infinitely divisible laws. Stochastics Integrals, Springer-verlag LNM 851, 285-370. Math. Review 82j:60149
  16. D. Revuz and M. Yor (1999), Continuous Martingales and Brownian motion, 3rd edition. Springer-Verlag Berlin Math. Review 2000h:60050
  17. L.C.G. Rogers (1981), Characterizing all diffusions with the 2M-X property. Ann. Prob. 9, 561-572. Math. Review 82j:60150
  18. P. Vallois (1991), La loi gaussienne inverse généralisée comme premier ou dernier temps de passage de diffusions. Bulletin des Sciences Mathématiques 115, 301-368. Math. Review 92k:60183
  19. S. Watanabe (1975), On time inversion of one-dimensional diffusion process. Zeitschrift für Wahr 31, 115-124. Math. Review 51#1983













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Electronic Communications in Probability. ISSN: 1083-589X