Title:
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Dirichlet functions of reflected Brownian motion (English) |
Author:
|
Engelbert, Hans-Jürgen |
Author:
|
Wolf, Jochen |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
125 |
Issue:
|
2 |
Year:
|
2000 |
Pages:
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235-247 |
Summary lang:
|
English |
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Category:
|
math |
. |
Summary:
|
We give a complete analytical characterization of the functions transforming reflected Brownian motions to local Dirichlet processes. (English) |
Keyword:
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Dirichlet process |
Keyword:
|
local time |
Keyword:
|
reflected Brownian motion |
MSC:
|
60G48 |
MSC:
|
60H99 |
MSC:
|
60J65 |
idZBL:
|
Zbl 0969.60043 |
idMR:
|
MR1768811 |
DOI:
|
10.21136/MB.2000.125954 |
. |
Date available:
|
2009-09-24T21:42:58Z |
Last updated:
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2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125954 |
. |
Reference:
|
[1] Assing S., Schmidt W.: Continuous Strong Markov Processes in Dimension 1 - A Stochastic Calculus Approach.Lecture Notes in Math. 1688, Springer, Berlin, 1998. MR 1724313, 10.1007/BFb0096157 |
Reference:
|
[2] Bertoin J.: Les processus de Dirichlet et tant qu' Espace de Banach.Stochastics 18 (1988), 155-168. MR 0861819, 10.1080/17442508608833406 |
Reference:
|
[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. Zbl 0646.60056, MR 0953117 |
Reference:
|
[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 0612544 |
Reference:
|
[5] Çinlar E., Jacod J., Protter P., Sharpe M. J.: Semimartingales and Markov processes.Z. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980), 161-219. Zbl 0443.60074, MR 0597337 |
Reference:
|
[6] Föllmer H.: Calcul d'Itô sans probabilités.Sém. Prob. XV, Lecture Notes in Math. 850. Springer, Berlin, 1981, pp. 143-150. Zbl 0461.60074, MR 0622559, 10.1007/BFb0088364 |
Reference:
|
[7] Föllmer H.: Dirichlet processes.Lecture Notes in Math. 851. Springer, Berlin, 1981, pp. 476-478. Zbl 0462.60046, MR 0621001, 10.1007/BFb0088738 |
Reference:
|
[8] Föllmer H., Protter P., Shiryaev A.N.: Quadratic covariation and an extension of Itô's formula.Bernoulli 1 (1995), 149-169. MR 1354459, 10.2307/3318684 |
Reference:
|
[9] Fukuskima M., Oshima Y., Takeda M.: Dirichlet Forms and Symmetric Markov Processes.Walter de Gruyter, Berlin, 1994. MR 1303354 |
Reference:
|
[10] Protter P.: Stochastic Integration and Differential Equations.Springer, Berlin, 1992. |
Reference:
|
[11] Revuz D., Yor M.: Continuous Martingales and Brownian Motion.2nd edition, Springer, Berlin, 1994. Zbl 0804.60001, MR 1303781 |
Reference:
|
[12] Russo F., Vallois P.: Forward, backward and symmetric stochastic integration.Probab. Theory Related Fields 97 (1993), 403-421. Zbl 0792.60046, MR 1245252, 10.1007/BF01195073 |
Reference:
|
[13] Russo F., Vallois P.: The generalized covariation process and Itô formula.Stochastic Process. Appl. 59 (1995), 81-104. Zbl 0840.60052, MR 1350257, 10.1016/0304-4149(95)93237-A |
Reference:
|
[14] Russo F., Vallois P.: Itô formula for $C^1$ -functions of semimartingales.Probab. Theory Related Fields 104 (1996), 27-41. MR 1367665, 10.1007/BF01303801 |
Reference:
|
[15] Schmidt W.: Über streng Markovsche stetige Semimartingale.Habilitationsschrift. Friedrich-Schiller-Universität, Jena. |
Reference:
|
[16] Schmidt W.: On stochastic differential equations with reflecting barriers.Math. Nachr. 142 (1989), 135-148. Zbl 0699.60043, MR 1017375, 10.1002/mana.19891420109 |
Reference:
|
[17] Wolf J.: Zur stochastischen Analysis stetiger lokaler Dirichletprozesse.Dissertation. Friedrich-Schiller-Universität, Jena. Zbl 0879.60061 |
Reference:
|
[18] Wolf J.: Transformations of semimartingales and local Dirichlet processes.Stochastics Stochastics Rep. 62 (1997), 65-101. Zbl 0890.60043, MR 1489182, 10.1080/17442509708834128 |
Reference:
|
[19] Wolf J.: An Itô formula for local Dirichlet processes.Stochastics Stochastics Rep. 62 (1997), 103-115. Zbl 0890.60044, MR 1489183, 10.1080/17442509708834129 |
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