Brownian analogues of Burke's theorem

Stochastic Processes and their Applications

Volumn 96, Issue 2, 2001, Pages 285-304

  O'Connell, Neil ^a   Yor, Marc ^b  

^a HEWLETT PACKARD LABORATORIES   (United Kingdom)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000804956     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(01)00119-3     Document Type: Article

References (43)

1. Abramowitz, M., Stegun, I.A., 1970. Handbook of Mathematical Functions, 9th Edition. Dover, New York.
2. Asmussen S. Applied Probability and Queues. 1987;Wiley, New York.
3. Baccelli, F., Borovkov, A., Mairesse, J., 2000. Asymptotic results on infinite tandem queueing networks. Probab. Theory Related Fields 118 (3), 365-405.
4. Baryshnikov Yu. GUES and QUEUES. Probab. Theory Related Fields. 119:2001;256-274.
5. Brémaud P. Point Processes and Queues: Martingale Dynamics. 1981;Springer, Berlin.
6. Burke P.J. The output of a queueing system. Oper. Res. 4(6):1956;699-704.
7. Carmona Ph., Petit F., Yor M. An identity in law involving reflecting Brownian motion, derived for generalized arc-sine laws for perturbed Brownian motions. Stochastic Process Appl. 79(2):1999;323-334.
8. Carmona Ph., Petit F., Yor M. Exponential functionals of Lévy processes. Barndorff-Nielsen O., Mikosch T., Resnick S. Lévy Processes: Theory and Applications. 2001;Birkhäuser, Basel.
9. Dembo A., Zeitouni O. Large Deviations Techniques and Applications. 2nd Edition:1998;Springer, Berlin.
10. Derrida B. Directed polymers in a random medium. Physica. A 163:1990;71-84.
11. Donati-Martin, C., Matsumoto, H., Yor, M., 2001. The law of geometric Brownian motion and its integral, revisited; application to conditional moments. Proceedings of the First Bachelier Conference, Springer, Berlin, to appear.
12. Dufresne D. An affine property of the reciprocal Asian option process. Research Paper No. 63, Centre for Actuarial Studies, Univ. Melbourne. Osaka Math. J. 38:2001;17-20.
13. Dufresne D. The integral of geometric Brownian motion. Adv. Appl. Probab. 33(1):2001;223-241.
14. Ganesh A.J. Large deviations of the sojourn time for queues in series. Ann. Oper. Res. 79:1998;3-26.
15. Glynn P.W., Whitt W. Departures from many queues in series. Ann. Appl. Probab. 1(4):1991;546-572.
16. Gravner, J., Tracy, C.A., Widom, H., 2000. Limit theorems for height fluctuations in a class of discrete space and time growth models. Preprint.
17. Hambly, B.M., Martin, J., O'Connell, N., 2001a. Concentration results for a Brownian directed percolation problem, Preprint.
18. Hambly, B.M., Martin, J., O'Connell, N., 2001b. Pitman's 2M-X theorem for skip-free random walks with Markovian increments, Electron. Comm. Probab., to appear.
19. Harrison J.M. Brownian Motion and Stochastic Flow Systems. 1985;Wiley, New York.
20. Harrison J.M., Williams R.J. On the quasireversibility of a multiclass Brownian service station. Ann. Probab. 18:1990;1249-1268.
21. Harrison J.M., Williams R.J. Brownian models of feedforward queueing networks: quasireversibility and product-form solutions. Ann. Appl. Probab. 2:1992;263-293.
22. Johansson K. Shape fluctuations and random matrices. Comm. Math. Phys. 209:2000;437-476.
23. Johnstone, I.M., 2000. On the distribution of the largest principal component. Preprint.
24. Kelly F.P. Reversibility and Stochastic Networks. 1979;Wiley, New York.
25. König, W., O'Connell, N., Roch, S., 2001. Non-colliding random walks, tandem queues and discrete orthogonal polynomial ensembles. Preprint.
26. Lebedev N. Special Functions and their Applications. 1972;Dover, New York.
27. Matsumoto H., Yor M. A version of Pitman's. 2M-X theorem for geometric Brownian motions C.R. Acad. Sci. Paris Sér. I. 328:1999;1067-1074.
28. Matsumoto H., Yor M. A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration. Osaka Math. J. 38:2001;1-16.
29. McKean, H.P., 2001. Brownian motion and the general diffusion: scale and clock. Proceedings of the First Bachelier Conference, Springer, Berlin, to appear.
30. Morse P.M. Stochastic properties of waiting lines. Oper. Res. 3:1955;256.
31. Muth E.G. The reversibility property of production lines. Management Sci. 25:1979;152-158.
32. Norros, I., Salminen, P., 2000. On unbounded Brownian storage. Preprint.
33. O'Brien G.G. Some queueing problems. J. Soc. Indust. Appl. Math. 2:1954;134.
34. O'Connell, N., 1999. Directed percolation and tandem queues. DIAS Technical Report DIAS-APG-9912.
35. O'Connell, N., Yor, M., 2001. A representation for non-colliding random walks. Electron. Comm. Probab., to appear.
36. Pitman J.W. One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Probab. 7:1975;511-526.
37. Pitman J.W., Rogers L.C.G. Markov functions. Ann. Probab. 9:1981;573-582.
38. Robert Ph. Réseaux et Files D'attente: Méthodes Probabilistes. Mathematics and Applications, Vol. 35. 2000;Springer, Berlin.
39. Seppäläinen T. Hydrodynamic scaling, convex duality, and asymptotic shapes of growth models. Markov Proc. Related Fields. 4:1998;1-26.
40. Szczotka W., Kelly F.P. Asymptotic stationarity of queues in series and the heavy traffic approximation. Ann. Probab. 18:1990;1232-1248.
41. Williams D. Path decomposition and continuity of local time for one-dimensional diffusions I. Proc. London Math. Soc. 28(3):1974;738-768.
42. Williams R.J. On the approximation of queueing networks in heavy traffic. Kelly F., Zeidens I. Stochastic Networks. 1996;Oxford University Press, Oxford.
43. Yor, M., 1992. Some Aspects of Brownian Motion, Part I: Some Special Functionals. Lecture notes in Mathematics, ETH Zürich, Birkhäuser, 1992.