A family of integral representations for the brownian variables

Nathalie Eisenbaum; Yueyun Hu

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 6, page 1083-1096
  • ISSN: 0246-0203

How to cite

top

Eisenbaum, Nathalie, and Hu, Yueyun. "A family of integral representations for the brownian variables." Annales de l'I.H.P. Probabilités et statistiques 39.6 (2003): 1083-1096. <http://eudml.org/doc/77789>.

@article{Eisenbaum2003,
author = {Eisenbaum, Nathalie, Hu, Yueyun},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Brownian motion; integral representation; flow; area integral},
language = {eng},
number = {6},
pages = {1083-1096},
publisher = {Elsevier},
title = {A family of integral representations for the brownian variables},
url = {http://eudml.org/doc/77789},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Eisenbaum, Nathalie
AU - Hu, Yueyun
TI - A family of integral representations for the brownian variables
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 6
SP - 1083
EP - 1096
LA - eng
KW - Brownian motion; integral representation; flow; area integral
UR - http://eudml.org/doc/77789
ER -

References

top
  1. [1] R.F. Bass, K. Burdzy, Stochastic bifurcation models, Ann. Probab.27 (1999) 50-108. Zbl0943.60087MR1681142
  2. [2] N. Bouleau, Sur la variation quadratique de certaines mesures vectorielles, Z. Wahrsch. Verw. Gebiete61 (1982) 283-290. Zbl0492.60078MR675617
  3. [3] K. Burdzy, Z.Q. Chen, Local time flow related to skew Brownian motion, Ann. Probab.29 (2001) 1693-1715. Zbl1037.60057MR1880238
  4. [4] N. Eisenbaum, Integration with respect to local time, Potential Anal.13 (2000) 303-328. Zbl0964.60062MR1804175
  5. [5] Y. Hu, J. Warren, Ray–Knight theorems related to a stochastic flow, Stochastic Process. Appl.86 (2000) 287-305. Zbl1028.60075
  6. [6] Th. Jeulin, Ray–Knight's theorem on Brownian local times and Tanaka's formula, in: Sem. Stochastic Proc. 1983 (Gainesville, FA), Birkhäuser, Boston, 1984, pp. 131-142. Zbl0561.60077
  7. [7] I. Karatzas, J.P. Lehoczky, S.E. Shreve, G.L. Xu, Optimality conditions for utility maximization in an incomplete market, in: Analysis and Optimization of Systems (Antibes, 1990), Lecture Notes in Control and Inform. Sci., 144, Springer, Berlin, 1990, pp. 3-23. Zbl0704.90015MR1070722
  8. [8] P. McGill, Integral representation of martingales in the Brownian excursion filtration, in: Sém. Probab. XX 1984/85, Lecture Notes in Math., 1204, Springer, Berlin, 1986, pp. 465-502. Zbl0635.60057MR942039
  9. [9] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, New York, 1998. Zbl0731.60002
  10. [10] L.C.G. Rogers, Continuity of martingales in the Brownian excursion filtration, Probab. Theory Related Fields76 (1987) 291-298. Zbl0611.60075MR912655
  11. [11] L.C.G. Rogers, J.B. Walsh, A(t,Bt) is not a semimartingale, in: Seminar on Stochastic Processes (Vancouver, BC, 1990), Progr. Probab., 24, Birkhäuser, Boston, 1991, pp. 275-283. Zbl0721.60089MR1118450
  12. [12] L.C.G. Rogers, B. Walsh J, Local time and stochastic area integrals, Ann. Probab.19 (1991) 457-482. Zbl0729.60073MR1106270
  13. [13] L.C.G. Rogers, J.B. Walsh, The intrinsic local time sheet of Brownian motion, Probab. Theory Related Fields88 (1991) 363-379. Zbl0722.60079MR1100897
  14. [14] L.C.G. Rogers, J.B. Walsh, The exact 4/3-variation of a process arising from Brownian motion, Stochastics51 (3–4) (1994) 267-291. Zbl0851.60077
  15. [15] D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979. Zbl0426.60069MR532498
  16. [16] J.B. Walsh, Stochastic integration with respect to local time, in: Seminar Stoch. Processes, 1982 (Evanston, IL, 1982), Progr. Probab. Statist., 5, Birkhäuser, Boston, 1983, pp. 237-302. Zbl0524.60074MR733675
  17. [17] D. Williams, Conditional excursion theory, in: Séminaire de Probab. XIII, Lecture Notes in Math., 721, Springer, Berlin, 1979, pp. 490-494. Zbl0422.60058MR544819
  18. [18] M. Yor, Some Aspects of Brownian Motion. Part II: Some Recent Martingale Problems, Birkhäuser, Berlin, 1997. Zbl0880.60082MR1442263

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.