Some Absolute Continuity Relationships for Certain Anticipative Transformations of Geometric Brownian Motions

Publications of the Research Institute for Mathematical Sciences

Volumn 37, Issue 3, 2001, Pages 295-326

  Donati Martin, Catherine ^a   Matsumoto, Hiroyuki ^b   Yor, Marc ^c  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b NAGOYA UNIVERSITY   (Japan)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000929223     PISSN: 00345318     EISSN: None     Source Type: Journal    
DOI: 10.2977/prims/1145477226     Document Type: Article

References (20)

1. Beneš, V. E., Nonexistence of strong nonanticipating solutions to stochastic DE's: implications for functional DE's, filtering, and control, Stoch. Proc. Appl., 5 (1977), 243–263.
2. Beneš, V. E., Realizing a weak solution on a probability space, Stoch. Proc. Appl., 7 (1978), 205–225.
3. Beneš, V. E., Realizing a weak solution on a probability space, in Measure Theory Application to Stochastic Analysis, Ed. by G. Kallianpur and D. Kölzow, 101–113, Lec. Notes in Math., 695, Springer-Verlag, 1978.
4. Buckdahn, R. and Föllmer, H., A conditional approach to the anticipating Girsanov transformation, Prob. Theory. Relat. Fields, 95 (1993), 311–330.
5. Donati-Martin, C., Equations différentielles stochastiques dans R avec conditions aux bords, Stochastics Stochastics Rep., 35 (1991), 143–173.
6. Dufresne, D., The distribution of a perpetuity, with application to risk theory and pension funding, Scand. Actuar. J., No.1–2 (1990), 39–79.
7. Dufresne, D., An affine property of the reciprocal Asian option process, Osaka J. Math., 38 (2001), 379–381.
8. Föllmer, H. and Imkeller, P., Anticipation cancelled by a Girsanov transformation: a paradox on Wiener space, Ann. Inst. H. Poincaré, Prob. Stat., 29 (1993), 569–586.
9. Kusuoka, S., The nonlinear transformation of Gaussian measures on Banach space and its absolute continuity, J. Fac. Sci., Univ. Tokyo Sect. IA, 29 (1982), 567–597.
10. Liptser, R. S. and Shiryayev, A. N., Statistics of Random Processes, I., general Theory, 2nd Ed., Springer-Verlag, Berlin, 2001.
11. Matsumoto, H. and Yor, M., A version of Pitman's 2M - X theorem for geometric Brownian motions, C. R. Acad. Sc. Paris, 328 (1999), 1067–1074.
12. Matsumoto, H. and Yor, M., A Relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration, Osaka J. Math., 38 (2001), 383–398.
13. Matsumoto, H. and Yor, M., 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.
14. Matsumoto, H. and Yor, M., An analogue of Pitman's 2M -X theorem for exponential Wiener functionals, Part II: the role of the generalized inverse Gaussian laws, Nagoya Math. J., 162 (2001), 65–86.
15. Nualart, D., The Malliavin Calculus and Related Topics, Springer-Verlag, Berlin, 1995.
16. Nualart, D. and Pardoux, E., Boundary value problems for stochastic differential equations, Ann. Prob., 19 (1991), 1118–1144.
17. Ramer, R., On nonlinear transformations of Gaussian measures, J. Func. Anal., 15 (1974), 166–187.
18. Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion, 3rd. Ed., Springer-Verlag, Berlin, 1999.
19. Russo, E. and Vallois, P., Forward, backward and symmetric stochastic integration, Prob. T.H. Rel. Fields, 97 (1993), 403–421.
20. Yor, M., Sur certaines fonctionnelles exponentielles du mouvement brownien réel, J. Appl. Prob., 29 (1992), 202–208.