Some changes of probabilities related to a geometric brownian motion version of pitman’s 2m – x theorem

Electronic Communications in Probability

Volumn 4, Issue , 1999, Pages 15-23

  Matsumoto, Hiroyuki ^a,b  

^a NAGOYA UNIVERSITY   (Japan)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

(Strict) Local Martingale; Diffusion Process; Explosion; Geometric Brownian Motion; Markov Intertwining Kernel

Indexed keywords

EID: 0001779433     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v4-1001     Document Type: Article

References (17)

1. K. D. Elworthy, X-M. Li and M. Yor, On the tails of the supremum and the quadratic variation of strictly local martingales, Sem. Prob. XXXI, Lecture Notes Math. 1655, 113-125, Springer-Verlag, Berlin, 1997.
2. K. D. Elworthy, X-M. Li and M. Yor, The importance of strict local martingales, applications to radial Ornstein-Uhlenbeck processes, to appear in Prob. Th. Rel. Fields, 1999.
3. A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms, I, McGraw-Hill, New York, 1954.
4. W. Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. Math., 55 (1952), 468-519.
5. D. Kennedy, Some martingales related to cumulative sum tests and single-server queues, Stoch. Proc. Appl., 4 (1976), 261-269.
6. J. Kent, Some probabilistic properties of Bessel functions, Ann. Prob., 6 (1978), 760-770.
7. T. G. Kurtz, Martingale problems for conditional distributions of Markov processes, Elect. J. Prob., 3 (1998), 1-29.
8. M. N. Lebedev, Special Functions and their Applications, Dover, New York, 1972.
9. H. Matsumoto and M. Yor, A version of Piman’s 2M — X theorem for geometric Brownian motions, C. R. Acad. Sci. Paris, Serie I, 328 (1999), 1067-1074.
10. H. P. McKean, Jr., Stochastic Integrals, Academic Press, New York, 1969.
11. J. W. Pitman and M. Yor, Bessel processes and infinitely divisible laws, Stochastic Integrals, ed. by D.Williams, Lecture Notes Math. 851, 285-370, Springer-Verlag, Berlin, 1981.
12. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, 3rd. Ed., SpringerVerlag, Berlin, 1999.
13. L. C. G. Rogers and J. W. Pitman, Markov functions, Ann. Prob., 9 (1981), 573-582.
14. 1-boundedness and the uniform integrability of continuous martingales, to appear in Sem. Prob. XXXIII, Lecture Notes Math., Springer-Verlag, Berlin, 1999.
15. C. Yoeurp, Theoreme de Girsanov generalise et grossissement d’une filtration, in Grossissements de filtrations: exemples et applications, Ed. by, Th. Jeulin and M. Yor, Lecture Notes Math., 1118, 172-196, 1985.
16. M. Yor, Some Aspects of Brownian Motion, Part II: Some Recent Martingale Problems, Birkhauser, Basel, 1997.
17. S. Watanabe, On time inversion of one-dimensional diffusion processes, Z.W., 31 (1975), 115-124