Stationary excursions

Jim Pitman

Séminaire de probabilités de Strasbourg (1987)

  • Volume: 21, page 289-302

How to cite


Pitman, Jim. "Stationary excursions." Séminaire de probabilités de Strasbourg 21 (1987): 289-302. <>.

author = {Pitman, Jim},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {regenerative sets; Palm measure; stationary point processes; dual excursions},
language = {fre},
pages = {289-302},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Stationary excursions},
url = {},
volume = {21},
year = {1987},

AU - Pitman, Jim
TI - Stationary excursions
JO - Séminaire de probabilités de Strasbourg
PY - 1987
PB - Springer - Lecture Notes in Mathematics
VL - 21
SP - 289
EP - 302
LA - fre
KW - regenerative sets; Palm measure; stationary point processes; dual excursions
UR -
ER -


  1. Atkinson, B.W.and Mitro, J.B. (1983). Applications of Revuz and Palm type measures for additive functionals in weak duality. Seminar on stochastic processes1982. Birkhäuser, Boston. Zbl0528.60074MR733664
  2. Azema, J., Duflo, M. and Revuz, D. (1967). Mesure invariante sur les classes récurrentes des processus de Markov. Z. Wahrscheinlichkeitstheorie8, 157-181. Zbl0178.20302MR222955
  3. Azema, J., Duflo, M. and Revuz, D. (1969). Propriétés relatives des processus de Markov récurrents. Z. Wahrscheinlichkeitstheorie13, 286-314. Zbl0181.21002MR260015
  4. Biane, P. (1986). Relations entre pont et excursion du mouvement brownien réel. Ann. Inst. Henri. Poincaré, Prob. et Stat, 22, 1-7. Zbl0596.60079MR838369
  5. Bismut, J.M. (1985). Last exit decomposition and regularity at the boundary of transition probabilities. Z. Wahrscheinlichkeitstheorie69, 65-98. Zbl0551.60077MR775853
  6. Blumenthal, R.M. and Getoor, R.K. (1968). Markov processes and potential theory. Academic Press. Zbl0169.49204MR264757
  7. Burdzy, K. (1986). Brownian excursions from hyperplanes and smooth surfaces. T.A.M.S.295, 35-57. Zbl0601.60080MR831187
  8. Burdzy, K., Pitman, J.W. and Yor M., Asymptotic laws for crossings and excursions. Paper in preparation. Zbl0666.60070
  9. De Sam Lazaro, J. and Meyer, P.A. (1975). Hélices croissantes et mesures de Palm. Séminaire de Prob. IX pp. 38-51. Lecture Notes in Math.465. 
  10. Dynkin, E.B. (1985). An application of flows to time shift and time reversal in stochastic processes. T.A.M.S.287, 613-619. Zbl0562.60076MR768728
  11. Fitzsimmons, P.J. & Maisonneuve, B. (1986). Excessive measures and Markov processes with random birth and death. Probability Theory and Related Fields72, 319-336. Zbl0584.60085
  12. Franken, P., Konig, D., Arndt, V., Schmidt, V. (1981). Queues and point processes. Wiley and sons, New York. Zbl0505.60058
  13. Geman, D. & Horowitz, J.. (1973). Remarks on Palm measures. Ann. Inst. Henri Poincaré Sec B, IX213-232. Zbl0283.60056
  14. Getoor, R.K. (1979). Excursions of a Markov process. Ann. Probab. 7, 244-266. Zbl0399.60069MR525052
  15. Getoor, R.K. (1985). Some remarks on measures associated with homogeneous random measures. To appear. Sem. Stoch. Proc.1985. Birkhäuser, Boston. Zbl0604.60070MR896738
  16. Getoor, R.K. (1985). Measures that are translation invariant in one coordinate. Preprint. Zbl0617.28002MR902425
  17. Getoor, R.K. & Sharpe, M.J. (1981). Two results on dual excursions. Seminar on stochastic processes1981. Boston. p. 31-52. Birkhäuser. Zbl0531.60069
  18. Getoor, R.K. & Sharpe, M.J. (1982). Excursions of Dual processes. Adv. in Math. 45, 259-309 Zbl0497.60067
  19. Getoor, R.K. & Sharpe, M.J. (1984). Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheorie, 67, 1-62. Zbl0553.60070
  20. Getoor, R.K. & Steffens, J. (1985). Capacity theory without duality. Preprint Zbl0586.60069
  21. Greenwood, P. and Pitman, J.W. (1980a). Construction of local time and Poisson point processes from nested arrays. J. London Math. Soc. (2) 22, 182-192. Zbl0427.60048MR579823
  22. Greenwood, P. and Pitman, J.W. (1980b). Fluctuation identities for Lévy processes and splitting at the maximum. Adv. Appl. Prob.12, 893-902. Zbl0443.60037MR588409
  23. Hsu, P. (1986). On excursions of reflecting Brownian motion. To appear in T.A.M.S. Zbl0602.60070MR837810
  24. Itô, K. (1970). Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. pp. 225-239. Univ. of California Press, Berkeley. Zbl0284.60051MR402949
  25. Jacod, J. (1979). Calcul Stochastique et Problèmes de Martingales. Lecture Notes in Math.714, Springer-Verlag, Berlin. Zbl0414.60053MR542115
  26. Kaspi, H. (1983). Excursions of Markov processes: An approach via Markov additive processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 64, 251-268. Zbl0514.60073MR714146
  27. Kaspi, H. (1984). On invariant measures and dual excursions of Markov processes. Z. Wahrscheinlichkeitstheorie66, 185-204. Zbl0525.60076MR749221
  28. Kerstan, J., Matthes, K. and Mecke, J. (1974). Infinitely divisible point processes. Wiley and sons. New York. MR517931
  29. Kuznetsov, S.E. (1974). Construction of Markov processes with random times of birth and death. Th. Prob. Appl., 18, 571-574. Zbl0296.60049
  30. Maisonneuve, B. (1971). Ensembles régénératifs, temps locaux et subordinateurs. Sém. de Prob. V. Lecture Notes in Math191. MR448586
  31. Maisonneuve, B. (1975). Exit systems. Ann. Prob.3, 399-411. Zbl0311.60047MR400417
  32. Maisonneuve, B. (1983). Ensembles régénératifs de la droite. Z. Wahrscheinlichkeitstheorie63, 501-510. Zbl0496.60033MR705620
  33. Matthes, K. (1963/4). Stationäre zufällige Punktfolgen. Jahresbericht d. Deutsch. Math. Verein, 66, 66-79. Zbl0178.52803MR160265
  34. Mcfadden, J.A. (1962). On the lengths of intervals in a stationary point processJ. Roy. Stat. Soc. Ser. B, 24, 364-382. Zbl0201.50002MR153059
  35. Mecke, J. (1967). Stationäre zufällige Masse auf lokal kompakten Abelschen Gruppen. Z. Wahrscheinlichkeitstheorie9, 36-58. Zbl0164.46601MR228027
  36. Mitro, J.B. (1979). Dual Markov processes: Construction of a useful auxilliary process. Z. Wahrscheinlichkeitstheorie47, 139-156. Zbl0406.60067MR523166
  37. Mitro, J.B. (1984). Exit systems for dual Markov processes. Z. Wahrscheinlichkeitstheorie66, 259-267. Zbl0525.60075MR749225
  38. Neveu, J. (1968). Sur la structure des processes ponctuels stationaires. C. R. Acad. Sci, t 267, A p. 561. Zbl0164.19102MR233415
  39. Neveu, J. (1976). Sur les mesures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitstheorie verw. Geb.34, 199-203. Zbl0309.60037MR397873
  40. Neveu, J.. (1977). Ecole d'Eté de Probabilités de Saint-Flour VI-1976. 250-446. Lecture Notes in Math.598. Springer. Zbl0439.60044MR474493
  41. Pitman, J.W. (1981). Lévy systems and path decompositions. Seminar on stochastic processes1981. Birkhäuser, Boston. Zbl0518.60077MR647782
  42. Sharpe, M.J. (1972). Discontinuous additive functionals of dual Markov processes. Z. Wahrscheinlichkeitstheorie21, 81-95. Zbl0213.19404MR305491
  43. Taksar, M.I. (1980). Regenerative sets on the real line. Seminaire de probabilités XIV, SpringerLecture notes in math.784. Zbl0435.60014MR580147
  44. Taksar, M.I. (1981). Subprocesses of a stationary Markov process. Z. Wahrscheinlichkeitstheorie55, 275-299. Zbl0447.60056MR608022
  45. Taksar, M.I. (1983). Enhancing of semigroups. Z. Wahrscheinlichkeitstheorie63, 445-462. Zbl0545.60070MR705616
  46. Taksar, M.I. (1986). Infinite excessive and invariant measures. Preprint. Zbl0608.60071MR896746
  47. Totoki, H. (1966). Time changes of flows. Mem. Fac. Sci. Kyushu Univ. Ser. A., t 20, p. 27-55. Zbl0185.39103MR201606
  48. Vervaat, W. (1979). A relation between Brownian bridge and Brownian excursion. Ann. Prob.7, 143-149. Zbl0392.60058MR515820

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.