Conditioned stable Lévy processes and the lamperti representation

Journal of Applied Probability

Volumn 43, Issue 4, 2006, Pages 967-983

  Caballero, M E ^a   Chaumont, L ^b  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Conditioning to hit 0 continuously; Infinitesimal generator; Lamperti representation; Positive; Self similar Markov process; Stable L vy process; Stable L vy process conditioned to stay positive

Indexed keywords

EID: 33947276746     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1165505201     Document Type: Article

References (14)

1. BERTOIN, J. (1996). Lévy Processes. Cambridge University Press.
2. BERTOIN, J. (2002). Self-similar fragmentations. Ann. Inst. H. Poincaré Prob. Statist. 38, 319-340.
3. BINGHAM, N. H. (1973). Maxima of sums of random variables and suprema of stable processes. Z. Wahrscheinlichkeitsth. 26, 273-296.
4. BRYN-JONES, A. AND DONEY, R. A. (2006). A functional limit theorem for random walk conditioned to stay non-negative. J. London Math. Soc. 74, 244-258.
5. CARAVENNA, F. AND CHAUMONT, L. (2006). Invariances principles for conditioned random walks. Preprint 1050, LPMA.
6. CARMONA, P., PETIT, F. AND YOR, M. (2001). Exponential functionals of Lévy processes. In Lévy Processes, Birkhäuser, Boston, MA, pp. 41-55.
7. CHAUMONT, L. (1996). Conditionings and path decompositions for Lévy processes. Stoch. Process. Appl. 64, 39-54.
8. DONEY, R. A. (2005). Fluctuation theory for Lévy processes. To appear in École d'été de Probabilités de Saint-Flour.
9. DUQUESNE, T. AND LE GALL, J. F. (2002). Random Trees, Levy Processes and Spatial Branching Processes (Astérisque 281). Société Mathématique de France, Paris.
10. LAMPERTI, J. W. (1972). Semi-stable Markov processes. Z. Wahrscheinlichkeitsth. 22, 205-225.
11. LEWIS, A. AND MORDECKI, E. (2005). Wiener-Hopf factorization for Lévy processes having negative jumps with rational transforms. Tech. Rep.
12. RIVERO, V. (2005). Recurrent extensions of self-similar Markov processes and Cramér's condition. Bernoulli 11, 471-509.
13. SATO, K. I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.
14. ZOLOTAREV, V. M. (1986). One-Dimensional Stable Distributions (Transl. Math. Monogr. 65). American Mathematical Society, Providence, RI.