On lévy processes conditioned to stay positive

Electronic Journal of Probability

Volumn 10, Issue , 2005, Pages 948-961

  Chaumont, L ^a   Doney, R A ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Creeping; Excursion measure; L vy process conditioned to stay positive; Path decomposition; Weak convergence

Indexed keywords

EID: 23244454088     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v10-261     Document Type: Article

References (15)

1. J. Bertüin: Levy Processes, Cambridge University Press, Cambridge, (1996).
2. J. Bertüin: An extension of Pitman’s theorem for spectrally positive Levy processes. Ann. Probab. 20, no. 3, 1464-1483, (1992).
3. J. Bertüin: Splitting at the infimum and excursions in half-lines for random walks and Levy processes. Stoch. Process, Appl. 47, 17-35, (1993).
4. J. Bertüin and R.A. Düney: On conditioning a random walk to stay nonnegative. Ann. Probab. 22, no. 4, 2152-2167, (1994).
5. L. Chaümünt: Sur certains processus de Levy conditionnes a rester positifs. Stochastics and Stoch. Rep., 47, 1-20, (1994).
6. L. ChaüMünt: Conditionings and path decompositions for Levy processes. Stoch. Process. Appl. 64, 39-54, (1996).
7. R.A Düney: Tanaka’s construction of Levy processes conditioned to stay positive. Séminaire de Probabilités, vol XXXVIII, 1-4, Lecture Notes in Math., 1686, Springer, Berlin, 2005.
8. R.A Düney: Some excursion calculations for spectrally one-sided Levy processes. Séminaire de Probabilités, Vol XXXVIII, 5-15, Lecture Notes in Math., 1686, Springer, Berlin, 2005.
9. T. DüQüesne: Path decompositions for real Levy processes. Ann. Inst. H. Poincaré Probab. Statist. 39, no. 2, 339-370, (2003).
10. K. Hiranü: Levy processes with negative drift conditioned to stay positive. Tokyo J. Math., 24, 291-308, (2001).
11. P.W. Millar: Zero-one laws and the minimum of a Markov process. Trans. Amer. Math. Soc. 226, 365-391, (1977).
12. V. Riverü: Recouvrements aléatoires et processus de Markov autosimilaires. PhD Thesis. Universite Paris 6, (2004).
13. M. L. Silverstein: Classification of coharmonic and coinvariant functions for a Levy process. Ann. Probab. 8, 539-575, (1980).
14. H. Tanaka: Time reversal of random walks in one dimension. Tokyo J. Math. 12, 159-174, (1989).
15. H. Tanaka: Levy processes conditioned to stay positive and diffusions in random environments. Advanced Studies in Pure Mathematics, 39, 355-376, (2004).