Intersection Local Times and Tanaka Formulas

Richard F. Bass; Davar Khoshnevisan

Annales de l'I.H.P. Probabilités et statistiques (1993)

  • Volume: 29, Issue: 3, page 419-451
  • ISSN: 0246-0203

How to cite

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Bass, Richard F., and Khoshnevisan, Davar. "Intersection Local Times and Tanaka Formulas." Annales de l'I.H.P. Probabilités et statistiques 29.3 (1993): 419-451. <http://eudml.org/doc/77464>.

@article{Bass1993,
author = {Bass, Richard F., Khoshnevisan, Davar},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {renormalization; multiple points; double points; intersection local times; Brownian motion; additive functionals; Tanaka formula},
language = {eng},
number = {3},
pages = {419-451},
publisher = {Gauthier-Villars},
title = {Intersection Local Times and Tanaka Formulas},
url = {http://eudml.org/doc/77464},
volume = {29},
year = {1993},
}

TY - JOUR
AU - Bass, Richard F.
AU - Khoshnevisan, Davar
TI - Intersection Local Times and Tanaka Formulas
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1993
PB - Gauthier-Villars
VL - 29
IS - 3
SP - 419
EP - 451
LA - eng
KW - renormalization; multiple points; double points; intersection local times; Brownian motion; additive functionals; Tanaka formula
UR - http://eudml.org/doc/77464
ER -

References

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  1. [B1] R.F. Bass, Joint Continuity and Representations of Additive Functionals of d- Dimensional Brownian motion, Stock. Proc. Applic., Vol. 17, 1984, pp. 211-227. Zbl0543.60080MR751203
  2. [B2] R.F. Bass, A Probabilistic Approach to the Boundedness of Singular Integral Operators, in: Séminaire de Probabilités XXIV, Eds. J. AZÉMA and M. YOR, 15- 40, New York, Springer, 1980. Zbl0703.60065MR1071529
  3. [BK1] R.F. Bass, and D. Khoshnevisan, Local Times on Curves and Uniform Invariance Principles, Probab. Th. and rel. Fields, Vol. 92, 1992, pp. 465-492. Zbl0767.60070MR1169015
  4. [BK2] R.F. Bass and D. Khoshnevisan, Strong Approximations to Brownian Local Time, in: Seminar on Stochastic Processes1992, E. CINLAR, K. L. CHUNG and M. J. SHARPE Eds, Boston, Birkhäuser, 1993, pp. 43-65. Zbl0789.60062MR1278076
  5. [BG] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory. New York, Academic Press, 1968. Zbl0169.49204MR264757
  6. [Br] G.A. Brosamler, Quadratic Variation of Potentials and Harmonic Functions, Trans. Amer. Math. Soc., Vol. 149, 1970, pp. 243-257. Zbl0248.60057MR270442
  7. [Ch] K.L. Chung, A Course in Probability Theory, 2nd Ed., New York, Academic Press, 1974. Zbl0345.60003MR1796326
  8. [DM] C. Dellacherie and P.-A. Meyer, Probabilités et Potentiel : Théorie des Martingales, Paris, Hermann, 1980. Zbl0464.60001MR566768
  9. [Du] R.M. Dudley, Sample Functions of the Gaussian process, Ann. Probab., Vol. 1, 1973, pp. 66-103. Zbl0261.60033MR346884
  10. [Dy] E.B. Dynkin, Self-intersection Gauge for Random Walks and for Brownian Motion, Ann. Probab., Vol. 16, 1988, pp. 1-57. Zbl0638.60081MR920254
  11. [IM] K. Ito and H.P. Mckean, Diffusion Processes and their Sample Paths, New York, Springer, 1974. Zbl0285.60063MR345224
  12. [L] J.-F. Le Gall, Some Properties of Planar Brownian Motion, École d'été de Saint-Flour XX, New York, Springer, 1992. Zbl0779.60068MR1229519
  13. [ReY] D. Revuz and M. Yor, Continuous Martingales and Brownian Motion, New York, Springer, 1991. Zbl0731.60002MR1083357
  14. [R1] J. RosenTanaka's Formula for Multiple Intersections of Planar Brownian MotionStoch. Proc. and their Applic. Vol. 23, 1986, pp. 131-141. Zbl0612.60070MR866291
  15. [R2] J. RosenRandom Walks and Intersection Local Time, Ann. Probab., Vol. 18, 1990, pp. 959-977. Zbl0717.60057MR1062054
  16. [RY] J. Rosen and M. Yor, Tanaka Formulae and Renormalization for Triple Intersections of Brownian Motion in the Plane, Ann. Probab., Vol. 19, 1991, pp. 142-159. Zbl0719.60084MR1085330
  17. [Sh] N.-R. Shieh, White Noise Analysis and Tanaka Formula for Intersections of Planar Brownian Motion, Nagoya Math. J., Vol. 122, 1991, pp. 1-17. Zbl0759.60041MR1114018
  18. [Y] M. Yor, Compléments aux formules de Tanaka-Rosen, in: Séminaire de Probabilités XIX, J. AZÈMA, and M. YOR, New York, Springer, 1985, pp. 332-349. Zbl0563.60073MR889493

Citations in EuDML Documents

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  1. Jay Rosen, Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times
  2. Jay S. Rosen, Joint continuity of renormalized intersection local times
  3. Jay Rosen, Dirichlet processes and an intrinsic characterization of renormalized intersection local times
  4. Davar Khoshnevisan, Some polar sets for the brownian sheet
  5. Wendelin Werner, Sur les singularités des temps locaux d'intersection du mouvement brownien plan
  6. Jay S. Rosen, Continuous differentiability of renormalized intersection local times in R1
  7. Benoît Cadre, Une preuve «standard» du principe d'invariance de Stoll
  8. B. Cadre, Principes d’invariance faibles pour le temps local d’intersection du mouvement brownien de d

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