On reflecting brownian motion — a weak convergence approach

R. J. Williams; W. A. Zheng

Annales de l'I.H.P. Probabilités et statistiques (1990)

  • Volume: 26, Issue: 3, page 461-488
  • ISSN: 0246-0203

How to cite

top

Williams, R. J., and Zheng, W. A.. "On reflecting brownian motion — a weak convergence approach." Annales de l'I.H.P. Probabilités et statistiques 26.3 (1990): 461-488. <http://eudml.org/doc/77390>.

@article{Williams1990,
author = {Williams, R. J., Zheng, W. A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {normal reflection; Skorokhod representation; stationary reflecting Brownian motion; Dirichlet form; semimartingale representation},
language = {eng},
number = {3},
pages = {461-488},
publisher = {Gauthier-Villars},
title = {On reflecting brownian motion — a weak convergence approach},
url = {http://eudml.org/doc/77390},
volume = {26},
year = {1990},
}

TY - JOUR
AU - Williams, R. J.
AU - Zheng, W. A.
TI - On reflecting brownian motion — a weak convergence approach
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1990
PB - Gauthier-Villars
VL - 26
IS - 3
SP - 461
EP - 488
LA - eng
KW - normal reflection; Skorokhod representation; stationary reflecting Brownian motion; Dirichlet form; semimartingale representation
UR - http://eudml.org/doc/77390
ER -

References

top
  1. [1] R.F. Bass, P. Hsu, Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains, to appear in Ann. Prob.. Zbl0732.60090
  2. [2] R.F. Bass, P. Hsu, The semimartingale structure of reflecting Brownian motion, to appear in Proc. Am. Math. Soc. Zbl0694.60075MR1007487
  3. [3] P. Billingsley, Convergence of Probability Measures, John Wiley and Sons, new York, 1968. Zbl0172.21201MR233396
  4. [4] E. Carlen, Conservative diffusions, Comm. Math. Phys.94, 293-316. Zbl0558.60059MR763381
  5. [5] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
  6. [6] M. Fukushima, A construction of reflecting barrier Brownian motions for bounded domains, Osaka J. Math.4 (1967), 183-215. Zbl0317.60033MR231444
  7. [7] M. Fukushima, Dirichlet forms and Markov Processes, North-Holland, 1980. Zbl0422.31007MR569058
  8. [8] E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York, 1965. Zbl0137.03202MR367121
  9. [9] P. Hsu, Reflecting Brownian Motion, Boundary Local Time, and the Neumann Boundary Value Problem, Ph.D. Dissertation, Stanford, 1984. 
  10. [10] P.L. Lions, A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math.37 (1984), 511-537. Zbl0598.60060MR745330
  11. [11] T.J. Lyons, W.A. Zheng, A crossing estimate for the canonical process on a Dirichlet space and a tightness result, Colloque Paul Levy sur les Processus Stochastiques, Asterisque, 157-158 (1988), 249-271. Zbl0654.60059
  12. [12] P.A. Meyer, W.A. Zheng, Tightness criteria for laws of semimartingales, Ann. Inst. Henri Poincaré, 20 (1984), N°4, 357-372. Zbl0551.60046MR771895
  13. [13] Y. Saisho, Stochastic differential equations for multi-dimensional domain with reflecting boundary, Prob. Theor. Rel. Fields, 74 (1987), 455-477. Zbl0591.60049MR873889
  14. [14] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095
  15. [15] D.W. Stroock, S.R.S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math.24 (1971), 147-225. Zbl0227.76131MR277037
  16. [16] H. Tanaka, Stochastic differential equations with reflecting boundary conditions in convex regions, Hiroshima Math. J.9 (1979), 163-177. Zbl0423.60055MR529332
  17. [17] W.A. Zheng, Tightness results for laws of diffusion processes, Application to stochastic mechaniscs, Ann. Inst. Henri Poincaré21 (1985), 103-124. Zbl0579.60050MR798890
  18. [18] W.A. Zheng, Semimartingales in predictable random open sets, Séminaire de Probabilités XVI, Lect. Notes Math.920 (1982), Springer-Verlag, 370-379. Zbl0481.60054MR658698

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.