Dirichlet functions of reflected Brownian motion
Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 235-247

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes.
DOI : 10.21136/MB.2000.125954
Classification : 60G48, 60H99, 60J65
Keywords: Dirichlet process; local time; reflected Brownian motion
Engelbert, Hans-Jürgen; Wolf, Jochen. Dirichlet functions of reflected Brownian motion. Mathematica Bohemica, Tome 125 (2000) no. 2, pp. 235-247. doi: 10.21136/MB.2000.125954
@article{10_21136_MB_2000_125954,
     author = {Engelbert, Hans-J\"urgen and Wolf, Jochen},
     title = {Dirichlet functions of reflected {Brownian} motion},
     journal = {Mathematica Bohemica},
     pages = {235--247},
     year = {2000},
     volume = {125},
     number = {2},
     doi = {10.21136/MB.2000.125954},
     mrnumber = {1768811},
     zbl = {0969.60043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125954/}
}
TY  - JOUR
AU  - Engelbert, Hans-Jürgen
AU  - Wolf, Jochen
TI  - Dirichlet functions of reflected Brownian motion
JO  - Mathematica Bohemica
PY  - 2000
SP  - 235
EP  - 247
VL  - 125
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125954/
DO  - 10.21136/MB.2000.125954
LA  - en
ID  - 10_21136_MB_2000_125954
ER  - 
%0 Journal Article
%A Engelbert, Hans-Jürgen
%A Wolf, Jochen
%T Dirichlet functions of reflected Brownian motion
%J Mathematica Bohemica
%D 2000
%P 235-247
%V 125
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.125954/
%R 10.21136/MB.2000.125954
%G en
%F 10_21136_MB_2000_125954

[1] Assing S., Schmidt W.: Continuous Strong Markov Processes in Dimension 1 - A Stochastic Calculus Approach. Lecture Notes in Math. 1688, Springer, Berlin, 1998. | DOI | MR

[2] Bertoin J.: Les processus de Dirichlet et tant qu' Espace de Banach. Stochastics 18 (1988), 155-168. | DOI | MR

[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. | MR | Zbl

[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. | MR

[5] Çinlar E., Jacod J., Protter P., Sharpe M. J.: Semimartingales and Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980), 161-219. | MR | Zbl

[6] Föllmer H.: Calcul d'Itô sans probabilités. Sém. Prob. XV, Lecture Notes in Math. 850. Springer, Berlin, 1981, pp. 143-150. | DOI | MR | Zbl

[7] Föllmer H.: Dirichlet processes. Lecture Notes in Math. 851. Springer, Berlin, 1981, pp. 476-478. | DOI | MR | Zbl

[8] Föllmer H., Protter P., Shiryaev A.N.: Quadratic covariation and an extension of Itô's formula. Bernoulli 1 (1995), 149-169. | DOI | MR

[9] Fukuskima M., Oshima Y., Takeda M.: Dirichlet Forms and Symmetric Markov Processes. Walter de Gruyter, Berlin, 1994. | MR

[10] Protter P.: Stochastic Integration and Differential Equations. Springer, Berlin, 1992.

[11] Revuz D., Yor M.: Continuous Martingales and Brownian Motion. 2nd edition, Springer, Berlin, 1994. | MR | Zbl

[12] Russo F., Vallois P.: Forward, backward and symmetric stochastic integration. Probab. Theory Related Fields 97 (1993), 403-421. | DOI | MR | Zbl

[13] Russo F., Vallois P.: The generalized covariation process and Itô formula. Stochastic Process. Appl. 59 (1995), 81-104. | DOI | MR | Zbl

[14] Russo F., Vallois P.: Itô formula for $C^1$ -functions of semimartingales. Probab. Theory Related Fields 104 (1996), 27-41. | DOI | MR

[15] Schmidt W.: Über streng Markovsche stetige Semimartingale. Habilitationsschrift. Friedrich-Schiller-Universität, Jena.

[16] Schmidt W.: On stochastic differential equations with reflecting barriers. Math. Nachr. 142 (1989), 135-148. | DOI | MR | Zbl

[17] Wolf J.: Zur stochastischen Analysis stetiger lokaler Dirichletprozesse. Dissertation. Friedrich-Schiller-Universität, Jena. | Zbl

[18] Wolf J.: Transformations of semimartingales and local Dirichlet processes. Stochastics Stochastics Rep. 62 (1997), 65-101. | DOI | MR | Zbl

[19] Wolf J.: An Itô formula for local Dirichlet processes. Stochastics Stochastics Rep. 62 (1997), 103-115. | DOI | MR | Zbl

Cité par Sources :