Branching processes, the Ray-Knight theorem, and sticky brownian motion

Jonathan Warren

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 1-15

How to cite

top

Warren, Jonathan. "Branching processes, the Ray-Knight theorem, and sticky brownian motion." Séminaire de probabilités de Strasbourg 31 (1997): 1-15. <http://eudml.org/doc/113954>.

@article{Warren1997,
author = {Warren, Jonathan},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {Brownian motion; Bessel process; continuous-state branching process; stochastic differential equation},
language = {fre},
pages = {1-15},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Branching processes, the Ray-Knight theorem, and sticky brownian motion},
url = {http://eudml.org/doc/113954},
volume = {31},
year = {1997},
}

TY - JOUR
AU - Warren, Jonathan
TI - Branching processes, the Ray-Knight theorem, and sticky brownian motion
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 1
EP - 15
LA - fre
KW - Brownian motion; Bessel process; continuous-state branching process; stochastic differential equation
UR - http://eudml.org/doc/113954
ER -

References

top
  1. [1] M. Amir. Sticky Brownian motion as the strong limit of a sequence of random walks. Stochastic Processes and their Applications, 39:221-237, 1991. Zbl0744.60097MR1136247
  2. [2] R.J. Chitashvili. On the nonexistence of a strong solution in the boundary problem for a sticky Brownian motion. Technical Report BS-R8901, Centre for Mathematics and Computer Science, Amsterdam, 1989. Zbl0914.60026
  3. [3] W. Feller. On boundaries and lateral conditions for the Kolmogorov equations. Annals of Mathematics, Series 2, 65:527-570, 1957. Zbl0084.35503MR90928
  4. [4] J.M. Harrison and A.J. Lemoine. Sticky Brownian motion as the limit of storage processes. Journal of Applied Probability, 18:216-226, 1981. Zbl0453.60072MR598937
  5. [5] N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes. North Holand-Kodansha, Amsterdam and Tokyo, 1981. Zbl0495.60005MR637061
  6. [6] F.B. Knight. Essentials of Brownian motion and Diffusion, volume 18 of Mathematical Surveys. American Mathematical Society, Providence, Rhode-Island, 1981. Zbl0458.60002MR613983
  7. [7] J.F. Le GallCours de troisième cycle, Laboratoire de Probabilités, Paris 6. 1994. 
  8. [8] J.W. Pitman and M. Yor. A decomposition of Bessel bridges. Zeitschrift für Wahrscheinlichkeitstheorie, 59:425-457, 1982. Zbl0484.60062MR656509
  9. [9] D. Revuz and M. Yor. Continuous martingales and Brownian motion. Springer, Berlin, 1991. Zbl0731.60002MR1083357
  10. [10] L.C.G. Rogers and D. Williams. Diffusions, Markov processes and Martingales, vol 2: Itô calculus. Wiley, New York, 1987. Zbl0627.60001MR921238
  11. [11] T. Shiga and S. Watanabe. Bessel diffusions as a one-parameter family of diffusion processes. Zeitschrift für Wahrscheinlichkeitstheorie, 27:37-46, 1973. Zbl0327.60047MR368192
  12. [12] K. Yamada. Reflecting or sticky Markov processes with Lévy generators as the limit of storage processes. Stochastic Processes and their Applications, 52:135-164, 1994. Zbl0811.60067MR1289173
  13. [13] M. Yor. Some remarks concerning sticky Brownian motion. Unpublished, 1989. 
  14. [14] M. Yor. Some aspects of Brownian motion, part 1: Some special functionals. Birkhäuser, 1992. Zbl0779.60070MR1193919

NotesEmbed ?

top

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.