On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum

Journal of Theoretical Probability

Volumn 17, Issue 1, 2004, Pages 183-220

  Pistorius, M R ^a  

^a KING'S COLLEGE LONDON   (United Kingdom)

Author keywords

Excursion theory; Exponential decay; First passage; h transform; Reflected L vy process

Indexed keywords

EID: 4043174902     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTP.0000020481.14371.37     Document Type: Article

References (28)

1. Asmussen, S. (1989). Applied Probability and Queues, Wiley series in probability.
2. Avram, F., Kyprianou, A. E., and Pistorius, M. R. (2004). Exit problems for spectrally negative Lévy processes and applications to (Canadized) Russian options. Ann. Appl. Probab. (forthcoming).
3. Bertoin, J. (1991). Sur la décomposition de la trajectoire d'un processus de Lévy spectralement positif en son infimum. Ann. Inst. H. Poincaré Probab. Statist. 27, 537-547.
4. Bertoin, J. (1996). On the first exit time of a completely asymmetric stable process from a finite interval. Bull. London Math. Soc. 28, 514-520.
5. Bertoin, J. (1996). Lévy Processes, Cambridge University Press.
6. Bertoin, J. (1997). Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval. Ann. Appl. Probab. 7, 156-169.
7. Bingham, N. H. (1975). Fluctuation theory in continuous time. Adv. Appl. Prob. 7, 705-766.
8. Borovkov, A. A. (1976). Stochastic Processes in Queueing Theory, Springer-Verlag.
9. Borodin, A. N., and Salminen, P. (1996). Handbook of Brownian Motion - Facts and Formulae, Birkhäuser.
10. Chaumont, L. (1993). Sur certains processus de Lévy conditionés à rester positifs. Stochastics Stochastic Rep. 47, 1-20.
11. Chung, K. L. (1986). Doubly Feller process with multiplicative functional. In Seminar on Stochastic Processes, Birkhäuser, pp. 63-78.
12. Dellacherie, C., and Meyer, P. A. (1987). Probabilités et potentiel (tome 4), Hermann Paris.
13. Emery, D. J. (1973). Exit problem for a spectrally positive process. Adv. in Appl. Probab. 5, 498-520.
14. Hawkes, J. (1979). Potential theory of Lévy processes. Proc. London Math. Soc. 38, 335-352.
15. Jacod, J., and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes, Springer-Verlag.
16. Knight, F. B. (1969). Brownian local times and taboo processes. Trans. Amer. Soc 73, 173-185.
17. Kyprianou, A. E., and Pistorius, M. R. (2003). Perpetual options and Canadization through fluctuation theory. Ann. Appl. Probab. 13, 1077-1098.
18. Lambert, A. (2000). Completely asymmetric Lévy processes confined in a finite interval. Ann. Inst. H. Poincaré Prob. Stat. 36, 251-274.
19. Winkel, M. (2002). Right inverses of non-symmetric Lévy processes. Ann. Probab. 30, 382-415.
20. Prabhu, N. U. (1997). Insurance, Queues, Dams, Springer-Verlag.
21. Robbins, H., and Siegmund, D. (1972). On the law of the iterated logarithm for maxima and minima. Proc. Sixth Berkerley Symp. 3, 51-70.
22. Protter, P. (1990). Stochastic Integration and Differential Equations, Springer-Verlag.
23. Rogers, L. C. G. (1984). On a new identity for real Lévy processes. Ann. Inst. Henri Poincaré 20, 21-34.
24. Spitzer, F. (1964). Principles of Random Walks, Van Nostrand, Princeton.
25. Suprun, V. N. (1976). The ruin problem and the resolvent of a killed independent increment process. Ukrainian Math. J. 28, 39-45.
26. Takács, L. (1966). Combinatorial Methods in the Theory of Stochastic Processes, Wiley, New York.
27. Tucker, H. G. (1962). Absolute continuity of infinitely divisible distributions. Pacific J. Math. 12, 1125-1129.
28. Tuominen, P., and Tweedie, R. (1979). Exponential decay and ergodic properties of general Markov processes. Adv. Appl. Prob. 11, 784-803.