Markov jump processes with a singularity

Advances in Applied Probability

Volumn 32, Issue 3, 2000, Pages 779-799

  Barndorff Nielsen, Ole E ^a   Benth, Fred Espen ^a   Jensen, Jens Ledet ^a  

^a MaPhySto   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; LASER APPLICATIONS; STATE SPACE METHODS; STATISTICAL MECHANICS;

CONFLUENT HYPERGEOMETRIC FUNCTION; LASER COOLING; RENEWAL THEORY;

MARKOV PROCESSES;

EID: 0034266753     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800010259     Document Type: Article

References (14)

1. BARDOU, F. AND CASTIN, Y. (1998). Le refroidissement laser subrecul: fonctions d'onde stochastiques et vols de Lévy. In Images de la Physique (Revue de CNRS). CNRS, Paris, pp. 7-14.
2. BARDOU, F., BOUCHAUD, J.-P., ASPECT, A. AND COHEN-TANNOUDJI, C. (2000). Non-ergodic cooling: subrecoil laser cooling and Lévy statistics. Preprint.
3. BARDOU, F., BOUCHAUD, J. P., EMILE, O., ASPECT, A. AND COHEN-TANNOUDJI, C. (1994). Subrecoil laser cooling and Lévy flights. Phys. Rev. Lett. 72, 203-206.
4. BARNDORFF-NIELSEN, O. E. AND BENTH, F. E. (2000). Laser cooling and stochastics. To appear in State of the Art in Probability and Statistics; Festschrift for Willem R. van Zwet (Lecture Notes - Monograph Series), eds M. C. M. de Gunst, C. A. J. Klaassen and A. W. van der Vaart. Inst. Math. Statist, Beachwood, OH.
5. BARNDORFF-NIELSEN, O. E., BENTH, F. E. AND JENSEN, J. L. (2000). Light, atoms, and singularities. MaPhySto Res. Rept 19, University of Aarhus. Submitted.
6. BINGHAM, N. H., GOLDIE, C. M. AND TEUGELS, J. L. (1987). Regular Variation. Cambridge University Press.
7. CRUMP, K. S. (1970a). On systems of renewal equations: the reducible case. J. Math. Anal. Appl. 31, 517-528.
8. CRUMP, K. S. (1970b). On systems of renewal equations. J. Math. Anal. Appl. 30, 425-434.
9. ERICKSON, K. B. (1970). Strong renewal theorems with infinite mean. Trans. Amer. Math. Soc. 151, 263-291.
10. FELLER, W. (1966). An Introduction to Probability Theory and its Applications. John Wiley, New York.
11. MODE, C. J. (1971). Applications of the Fredholm theory in Hilbert space to infinite systems of renewal type integral equations. Math. Biosci. 12, 347-368.
12. MODE, C. J. (1972). Limit theorems for infinite systems of renewal type integral equations arising in age-dependent branching processes. Math. Biosci. 13, 165-177.
13. SAUBAMÉA, B., LEDUC, M. AND COHEN-TANNOUDJI, C. (1999). Experimental investigation of the non-ergodic effects in subrecoil laser cooling. Phys. Rev. Lett. 83, 3796-3799.
14. SCHUMITZKY, A. AND WENSKA, T. (1975). An operator residue theorem with applications to branching processes and renewal type integral equations. SIAM J. Math. Anal. 6, 229-235.