Some remarks on Pitman's theorem

Bernhard Rauscher

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 266-271

How to cite


Rauscher, Bernhard. "Some remarks on Pitman's theorem." Séminaire de probabilités de Strasbourg 31 (1997): 266-271. <>.

author = {Rauscher, Bernhard},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {local martingale},
language = {eng},
pages = {266-271},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Some remarks on Pitman's theorem},
url = {},
volume = {31},
year = {1997},

AU - Rauscher, Bernhard
TI - Some remarks on Pitman's theorem
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 266
EP - 271
LA - eng
KW - local martingale
UR -
ER -


  1. [1] J. Bertoin. Sur la décomposition de la trajectoire d'un processus de Lévy spectralement positif en son infimum. Ann. Inst. Henri Poincaré, Probab. Stat. 274 (1991) 537-547. Zbl0758.60073MR1141246
  2. [2] J. Bertoin. An extension of Pitman's theorem for spectrally positive Lévy processes. Ann. Probab.203 (1992) 1464-1483. Zbl0760.60068MR1175272
  3. [3] P. Biane. Quelques proprietes du mouvement Brownien dans un cone. Stochastic Processes Appl.532 (1994) 233-240. Zbl0812.60067MR1302912
  4. [4] T. Jeulin. Un théorème de J. W. Pitman. Séminaire de Probabilités XIII. Lect. Notes in Math.721. Springer, Berlin Heidelberg New York (1979) 521-531. Zbl0422.60028MR544821
  5. [5] T. Jeulin. Semi-martingales et grossissement d'une filtration. Lect. Notes in Math.833. Springer, Berlin Heidelberg New York (1980). Zbl0444.60002MR604176
  6. [6] J.W. Pitman. One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. Appl. Prob.7 (1975) 511-526. Zbl0332.60055MR375485
  7. [7] D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. 2nd edition. Berlin: Springer, 1994. Zbl0804.60001MR1303781
  8. [8] L.C.G. Rogers. Characterizing all diffusions with the 2M — X property. Ann. Prob.9 (1981) 561-572. Zbl0465.60063MR624683
  9. [9] L.C.G. Rogers and J.W. Pitman. Markov functions. Ann. Prob.9 (1981) 573-582. Zbl0466.60070MR624684
  10. [10] P. Salminen. Mixing Markovian Laws; With an Application to Path Decompositions. Stochastics9 (1983) 223-231. Zbl0511.60069MR705472
  11. [11] Y. Saisho and H. Tanemura. Pitman type theorem for one-dimensional diffusion processes. Tokyo J. Math.13 (2) (1990) 429-440. Zbl0722.60082MR1088242
  12. [12] M.J. Sharpe. Local times and singularities of continuous local martingales. In: J. Azéma, P. A. Meyer and M. Yor (Eds.)Séminaire de Probabilités XIV. Lect. Notes in Math.784. Springer, Berlin Heidelberg New York (1980) 76-101. Zbl0428.60055MR580110
  13. [13] H. Tanaka. Time reversal of random walks in one dimension. Tokyo J. Math.12 (1989) 159-174. Zbl0692.60052MR1001739
  14. [14] H. Tanaka. Time reversal of random walks in Rd. Tokyo J. Math.13 (1989) 375-389. Zbl0734.60075MR1088238
  15. [15] K. Takaoka. On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem. To appear in: Séminaire de Probabilités XXXI. Lect. Notes in Math.Springer, Berlin Heidelberg New York (1997). Zbl0884.60075MR1478735
  16. [16] D. Williams. Path Decomposition and Continuity of Local Time for One-dimensional Diffusions, I. Proc. London Math. Soc. (3) 61 (1974) 738-768. Zbl0326.60093MR350881
  17. [17] M. Yor. Some Aspects of Brownian Motion. Part II: Some recent martingale problems. To appear: Lectures in Mathematics, ETHZürich, Basel: Birkhäuser. Zbl0880.60082MR1442263

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