A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet

Kyoto Journal of Mathematics

Volumn 49, Issue 4, 2009, Pages 785-815

  Hirsch, Francis ^a   Marc Yor, ^b  

^a UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77951279387     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1265899483     Document Type: Article

References (17)

1. J. Bertoin, Lévy Processes, Cambridge University Press, 1996.
2. D. Baker and M. Yor, A Brownian sheet martingale with the same marginals as the arithmetic average of geometric Brownian motion, Electron. J. Probab. 14-52 (2009), 1532-1540.
3. P. Carr, C.-O. Ewald and Y. Xiao, On the qualitative effect of volatility and duration on prices of Asian options, Finance Research Letters 5-3 (2008), 162-171.
4. R. C. Dalang and J. B. Walsh, The sharp Markov property of Levy sheets, Ann. Probab. 20-2 (1992), 591-626.
5. J. L. Doob, Generalized sweeping-out and probability, J. Funct. Anal. 2 (1968), 207-225.
6. N. Falkner and P. J. Fitzsimmons, Stopping distributions for right processes, Probab. Theory Related Fields 89-3 (1991), 301-318.
7. P. J. Fitzsimmons, Converse Jensen inequality, to appear in Rocky Mountain J. Math.
8. H. Föllmer, Martin boundaries on Wiener space, in: Diffusion Processes and Related Problems in Analysis, Vol.I: Diffusions in Analysis and Geometry, M. Pinsky ed., Progress in Probability n° 22, Birkhäuser, 1990, p. 3-16.
9. F. Hirsch and M. Yor, A construction of processes with one-dimensional martingale marginals, based upon path-space Ornstein- Uhlenbeck processes and the Brownian sheet, J. Math. Kyoto Univ. 49-2 (2009), 389-417.
10. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, 1987.
11. H. G. Kellerer, Markov-Komposition und eine Anwendung auf Martingale, Math. Ann. 14 (1971), 1-16.
12. D. B. Madan and M. Yor, Making Markov martingales meet marginals: with explicit constructions, Bernoulli 8-4 (2002), 509-536.
13. H. Rost, The stopping distribution of a Markov process, Invent. Math. 198 (1971), 99-122.
14. B. Roynette, Personal communication.
15. G. Samorodnitsky and M. S. Taqqu. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variation, Chapman &, Hall, 1994.
16. W. Schoutens, Stochastic Processes and Orthogonal Polynomials, Lect. Notes in Stat, n° 146, Springer, 2000.
17. V. Strassen, The existence of probability measures with given marginals, Ann. Math. Stat. 36 (1965), 423-439.