A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration

Osaka Journal of Mathematics

Volumn 38, Issue 2, 2001, Pages 383-398

  Matsumoto, Hiroyuki ^a   Yor, Marc ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

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EID: 0001033078     PISSN: 00306126     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. L. Alili, D. Dufresne and M. Yor: Sur l'identité de Bougerol pour les fonctionnelles exponentielles du mouvement brownien avac drift, in [37].
2. L. Alili and J.-C. Gruet: An explanation of a generalized Bougerol's identity in terms of hyperbolic Brownian motion, in [37].
3. P. Baldi, E. Casadio Tarabusi, A. Figa-Talamanca and M. Yor: Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities, to appear in Revista Math. Ibero-Americana (Madrid), 17 (2001).
4. Ph. Bougerol: Exemple de théorèmes locaux sur les groupes résolubles, Ann. Inst. H. Poincaré, 19 (1983), 369-391.
5. A. Comtet and C. Monthus: Diffusion in a one-dimensional random medium and hyperbolic Brownian motion, J. Phys. A: Math. Gen., 29 (1996), 1331-1345.
6. A. Comtet, C. Monthus and M. Yor: Exponential functionals of Brownian motion and disordered systems, J. Appl. Prob., 35 (1998), 255-271.
7. D. Dufresne: The distribution of a perpetuity, with application to risk theory and pension funding, Scand. Actuarial J., 1990, 39-79.
8. D. Dufresne: Algebraic Properties of Beta and Gamma Distributions, and applications, Adv. Appl. Math., 20 (1998), 285-299.
9. D. Dufresne: An affine property of the reciprocal Asian option process, Osaka J. Math. 38 (2001), 379-381.
10. H. Geman and M. Yor: Quelques relations entre processus de Bessel, options asiatiques et fonctions confluentes hypergéométriques, C. R. Acad. Sci. Paris, 314 (1992), 471-474.
11. H. Geman and M. Yor: Bessel processes, Asian options, and perpetuities, Math. Finance, 3 (1993), 349-375.
12. J.-C. Gruet: Semi-groupe du mouvement Brownien hyperbolique, Stochastics and Stochastic Reports, 56 (1996), 53-61.
13. N. Ikeda and H. Matsumoto: Brownian motion on the hyperbolic plane and Selberg trace formula, J. Func. Anal., 162 (1999), 63-110.
14. T. Jeulin: Semi-Martingales et Grossissement d'une Filtration, Lecture Notes Math. 833, Springer-Verlag, Berlin, 1980.
15. N-L. Johnson and S. Kotz: Continuous univariate distributions 1, John-Wiley & Sons, New-York, 1970.
16. K. Kawazu and H. Tanaka: On the maximum of a diffusion process in a drifted Brownian environment, in Sém. Prob. XXVII, Lecture Notes in Math. 1557, 78-85, Springer-Verlag, Berlin, 1991.
17. B. Leblanc: Une approche unifiee pour une forme exacte du prix d'une option dans les diffeents modeles a volatilite stochastique, Stochastic and Stochastic Reports, 57 (1996), 1-35.
18. H. Matsumoto and M. Yor: On Bougerol and Dufresne's identities for exponential Brownian functionals, Proc. Japan Acad., 74 Ser.A (1998), 152-155.
19. H. Matsumoto and M. Yor: A version of Pitman's 2M - X theorem for geometric Brownian motions, C. R. Acad. Sc. Paris, 328 (1999), 1067-1074.
20. 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.
21. H. Matsumoto and M. Yor: An analogue of Pitman's 2M - X theorem for exponential Wiener functionals, Part II: the role of the generalized inverse Gaussian laws, to appear in Nagoya Math. J., 162 (2001).
22. T. Nilsen and J. Paulsen: On the distribution of a randomly discounted compound Poisson process, Stoch. Proc. Appl., 61 (1996), 305-310.
23. N. O'Connell and M. Yor: Brownian analogues of Burke's theorem, to appear in Stoch. Proc. Appl.
24. J. Paulsen: Risk theory in a stochastic economic environment, Stoch. Proc. Appl., 46 (1993), 327-361.
25. K. Pearson: Contributions to the mathematical theory of evolution, II, Skew variation in homogeneous material, Phil. Trans. Royal Soc. London, Series A, 186 (1895), 343-414.
26. J.W. Pitman: One-dimensional Brownian motion and the three-dimensional Bessel process, Adv. Appl. Prob., 7 (1975), 511-526.
27. J.W. Pitman and M. Yor: Bessel processes and infinitely divisible laws, in Stochastic Integrals, ed. by D.Williams, Lecture Notes in Math. 851, 285-370, Springer-Verlag, Berlin, 1981.
28. D. Revuz and M. Yor: Continuous Martingales and Brownian Motion, 3rd. Ed., Springer-Verlag, Berlin, 1999.
29. D. Williams: Path decomposition and continuity of local time for one dimensional diffusions I, Proc. London Math. Soc., 28 (1974), 738-768.
30. E. Wong: The construction of a class of stationary Markov processes, in Proc. 16th Symposium of Appl. Math., 264-276, Amer. Math. Soc., Providence, 1964.
31. M. Yor: Some Aspects of Brownian Motion. Part II:Some Recent Martingale Problems, Birkhäuser, Basel, 1997.
32. n (n ≧ 3), Ann. Inst. Henri Poincaré, 21 (1984), 27-38.
33. M. Yor: On some exponential functionals of Brownian motion, Adv. Appl. Prob., 24 (1992). 509-531.
34. M. Yor: Sur les lois des fonctionnelles exponentielles du mouvement brownien, considérées en certains instants aléatoires, C. R. Acad. Sci. Paris, 314 (1992), 951-956.
35. M. Yor: Sur certaines fonctionnelles exponentielles du mouvement brownien réel, J. Appl. Prob., 29 (1992), 202-208.
36. M. Yor: Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity, in "Lévy Processes: Theory and Applications", ed. by O. Barndorff-Nielsen, T. Mikosch and S. Resnick, Birkhäser, (2001).
37. M. Yor (ed.): Exponential Functionals and Principal Values related to Brownian Motion, A collection of research papers, Biblioteca de la Revista Matemática Iberoamericana, Madrid, 1997.