Dirichlet functions of reflected Brownian motion

Hans-Jürgen Engelbert; Jochen Wolf

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 2, page 235-247
  • ISSN: 0862-7959

Abstract

top
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.

How to cite

top

Engelbert, Hans-Jürgen, and Wolf, Jochen. "Dirichlet functions of reflected Brownian motion." Mathematica Bohemica 125.2 (2000): 235-247. <http://eudml.org/doc/248682>.

@article{Engelbert2000,
abstract = {We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.},
author = {Engelbert, Hans-Jürgen, Wolf, Jochen},
journal = {Mathematica Bohemica},
keywords = {Dirichlet process; local time; reflected Brownian motion; Dirichlet process; local time; reflected Brownian motion},
language = {eng},
number = {2},
pages = {235-247},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dirichlet functions of reflected Brownian motion},
url = {http://eudml.org/doc/248682},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Engelbert, Hans-Jürgen
AU - Wolf, Jochen
TI - Dirichlet functions of reflected Brownian motion
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 2
SP - 235
EP - 247
AB - We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.
LA - eng
KW - Dirichlet process; local time; reflected Brownian motion; Dirichlet process; local time; reflected Brownian motion
UR - http://eudml.org/doc/248682
ER -

References

top
  1. Assing S., Schmidt W., 10.1007/BFb0096157, Lecture Notes in Math. 1688, Springer, Berlin, 1998. (1998) MR1724313DOI10.1007/BFb0096157
  2. Bertoin J., 10.1080/17442508608833406, Stochastics 18 (1988), 155-168. (1988) MR0861819DOI10.1080/17442508608833406
  3. Bertoin J., Une application du calcul du nombre de montées et de descentes aux fonctions de martingales locales continues, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 201-207. (1988) Zbl0646.60056MR0953117
  4. Bouleau N., Yor M., Sur la variation quadratique des temps locaux de certaines semi-martingales, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), 491-494. (1981) MR0612544
  5. Çinlar E., Jacod J., Protter P., Sharpe M. J., Semimartingales and Markov processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980), 161-219. (1980) Zbl0443.60074MR0597337
  6. Föllmer H., 10.1007/BFb0088364, Sém. Prob. XV, Lecture Notes in Math. 850. Springer, Berlin, 1981, pp. 143-150. (1981) Zbl0461.60074MR0622559DOI10.1007/BFb0088364
  7. Föllmer H., 10.1007/BFb0088738, Lecture Notes in Math. 851. Springer, Berlin, 1981, pp. 476-478. (1981) Zbl0462.60046MR0621001DOI10.1007/BFb0088738
  8. Föllmer H., Protter P., Shiryaev A.N., 10.2307/3318684, Bernoulli 1 (1995), 149-169. (1995) MR1354459DOI10.2307/3318684
  9. Fukuskima M., Oshima Y., Takeda M., Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. (1994) MR1303354
  10. Protter P., Stochastic Integration and Differential Equations, Springer, Berlin, 1992. (1992) 
  11. Revuz D., Yor M., Continuous Martingales and Brownian Motion, 2nd edition, Springer, Berlin, 1994. (1994) Zbl0804.60001MR1303781
  12. Russo F., Vallois P., 10.1007/BF01195073, Probab. Theory Related Fields 97 (1993), 403-421. (1993) Zbl0792.60046MR1245252DOI10.1007/BF01195073
  13. Russo F., Vallois P., 10.1016/0304-4149(95)93237-A, Stochastic Process. Appl. 59 (1995), 81-104. (1995) Zbl0840.60052MR1350257DOI10.1016/0304-4149(95)93237-A
  14. Russo F., Vallois P., 10.1007/BF01303801, Probab. Theory Related Fields 104 (1996), 27-41. (1996) MR1367665DOI10.1007/BF01303801
  15. Schmidt W., Über streng Markovsche stetige Semimartingale, Habilitationsschrift. Friedrich-Schiller-Universität, Jena. 
  16. Schmidt W., 10.1002/mana.19891420109, Math. Nachr. 142 (1989), 135-148. (1989) Zbl0699.60043MR1017375DOI10.1002/mana.19891420109
  17. Wolf J., Zur stochastischen Analysis stetiger lokaler Dirichletprozesse, Dissertation. Friedrich-Schiller-Universität, Jena. Zbl0879.60061
  18. Wolf J., 10.1080/17442509708834128, Stochastics Stochastics Rep. 62 (1997), 65-101. (1997) Zbl0890.60043MR1489182DOI10.1080/17442509708834128
  19. Wolf J., 10.1080/17442509708834129, Stochastics Stochastics Rep. 62 (1997), 103-115. (1997) Zbl0890.60044MR1489183DOI10.1080/17442509708834129

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.