Some polar sets for the brownian sheet

Davar Khoshnevisan

Séminaire de probabilités de Strasbourg (1997)

  • Volume: 31, page 190-197

How to cite


Khoshnevisan, Davar. "Some polar sets for the brownian sheet." Séminaire de probabilités de Strasbourg 31 (1997): 190-197. <>.

author = {Khoshnevisan, Davar},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {-parameter Brownian sheet; polar set},
language = {eng},
pages = {190-197},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Some polar sets for the brownian sheet},
url = {},
volume = {31},
year = {1997},

AU - Khoshnevisan, Davar
TI - Some polar sets for the brownian sheet
JO - Séminaire de probabilités de Strasbourg
PY - 1997
PB - Springer - Lecture Notes in Mathematics
VL - 31
SP - 190
EP - 197
LA - eng
KW - -parameter Brownian sheet; polar set
UR -
ER -


  1. [A1] R.J. Adler (1981). The Geometry of Random Fields, Wiley, London Zbl0478.60059MR611857
  2. [A2] R.J. Adler (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, Institute of Mathematical Statistics Lecture Notes—Monograph Series, Vol. 12 Zbl0747.60039MR1088478
  3. [BBK] R.F. Bass, K. Burdzy AND D. Khoshnevisan (1994). Intersection local time for points of infinite multiplicity, Ann. Prob., 22, 566-625 Zbl0814.60078MR1288124
  4. [BK] R.F. Bass AND D. Khoshnevisan (1993). Intersection local times and Tanaka formulas, Ann. Inst. Henri Poincaré: Prob. et Stat., 29, 419-451 Zbl0798.60072MR1246641
  5. [BG] R. Blumenthal AND R.K. Getoor (1968). Markov Processes and Potential Theory. Academic Press.New York Zbl0169.49204MR264757
  6. [C] X. Chen (1994). Hausdorff dimension of multiple points of the (N.d) Wiener process, Indiana Univ. Math. J.. 43(1), 55-60 Zbl0797.60065MR1275452
  7. [DEK1] A. Dvoretsky, P. Erdös AND S. Kakutani (1950). Double points of paths of Brownian motion in n-space, Acta. Sci. Math. (Szeged), 12. 74-81 Zbl0036.09001MR34972
  8. [DEK2] A. Dvoretsky, P. Erdös AND S. Kakutani (1954). Multiple points of Brownian motion in the plane, Bull. Res. Council Israel Section F, 3, 364-371 MR67402
  9. [DEKT] A. Dvoretsky, P. Erdös, S. Kakutani AND S.J. Taylor (1957). Triple points of Brownian motion in 3-space. Proc. Camb. Phil. Soc., 53, 856-862 Zbl0208.44103MR94855
  10. [D1] E.B. Dynkin (1988). Self-intersection gauge for random walks and for Brownian motion, Ann. Prob., 16, 1-57 Zbl0638.60081MR920254
  11. [D2] E.B. Dynkin (1985). Random fields associated with multiple points of Brownian motion, J. Funct. Anal., 62, 397-434 Zbl0579.60081MR794777
  12. [E] W. Ehm (1981). Sample function properties of multiparameter stable processes, Zeit. Wahr. verw. Geb., 56, 195-228 Zbl0471.60046MR618272
  13. [E1] S.N. Evans (1987) Multiple points in the sample paths of a Lévy process, Prob. Th. Rel. Fields, 76, 359-367 MR912660
  14. [E2] S.N. Evans (1987) Potential theory for a family of several Markov processes, Ann. Inst. Henri Poincaré: Prob. et Stat., 23, 499-530 Zbl0625.60086MR906728
  15. [FS-1] P.J. Fitzsimmons AND T.S. Salisbury (1989). Capacity and energy for multi-parameter Markov processes, Ann. Inst. Henri Poincaré: Prob. et Stat., 25, 325-350 Zbl0689.60071MR1023955
  16. [FS-2] P.J. Fitzsimmons AND T.S. Salisbury Forthcoming Manuscript. 
  17. [F] B. Fristedt (1995). Math. Reviews, review 95b:60100, February 1995 issue 
  18. [HaP] J. Hawkes AND W.E. Pruitt (1974). Uniform dimension results for processes with independent increments, Zeit. Wahr. verw. Geb., 28, 277-288 Zbl0268.60063MR362508
  19. [H] W.J. Hendricks (1974). Multiple points for transient symmetric Lévy processes, Zeit. Wahr. verw. Geb.49, 13-21 Zbl0398.60042MR539660
  20. [K] J.P. Kahane (1985). Some Random Series of Functions, Cambridge Univ. Press, Cambridge, U.K. Zbl0571.60002MR833073
  21. [Ka] R. Kaufman (1969). Une propriété métrique du mouvement brownien, C.R. Acad. Sci.Paris, Sér. A, 268, 727-728 Zbl0174.21401MR240874
  22. [LG] J.F. Legall (1990). Some Properties of Planar Brownian Motion, Ecole d'été de Probabilités de St-Flour XX, LNM1527, 111-235 Zbl0779.60068MR1229519
  23. [OP] S. Orey AND W.E. Pruitt (1973). Sample functions of the N-parameter Wiener process, Ann. Prob., 1, 138-163 Zbl0284.60036MR346925
  24. [P] Y. Peres (1995). Intersection-equivalence of Brownian paths and certain branching processes, Comm. Math. Phys. (To appear) Zbl0851.60080MR1384142
  25. [R1] J. Rosen (1995). Joint continuity of renormalized intersection local times. Preprint 
  26. [R2] J. Rosen (1984). Stochastic integrals and intersections of Brownian sheet. Unpublished manuscript 
  27. [R3] J. Rosen (1984). Self-intersections of random fields, Ann. Prob., 12. 108-119 Zbl0536.60066MR723732
  28. [S] T.S. Salisbury (1995). Energy. and intersections of Markov chains, Proceedings of the IMA Workshop on Random Discrete Structures (To appear) Zbl0845.60068MR1395618
  29. [Sh] N.-R. Shieh (1991). White noise analysis and Tanaka formulae for intersections of planar Brownian motion, Nagoya Math. J., 122, 1-17 Zbl0759.60041MR1114018
  30. [T1] S.J. Taylor (1986). The measure theory of random fractals. Math. Proc. Camb. Phil. Soc., 100. 383-406 Zbl0622.60021MR857718
  31. [T2] S.J. Taylor (19). Multiple points for the sample paths of a transient stable process, J. Math. Mech., 16, 1229-1246 Zbl0178.19301
  32. [T3] S.J. Taylor (1966). Multiple points for the sample paths of the symmetric stable process, Zeit. Wahr. verw. Geb., 5, 247-264 Zbl0146.37905MR202193
  33. [V] S.R.S. Varadhan (1969). Appendix to "Euclidean Quantum Field Theory", by K. Symanzik. In Local Quantum Theory (ed.: R. Jost). Academic Press, New York 
  34. [W] W. Werner (1993). Sur les singularités des temps locaux d'intersection du mouvement brownien plan, Ann. Inst. Henri. Poincaré: Prob. et Stat., 29, 391-418 Zbl0798.60071MR1246640
  35. [Y] M. Yor (1985). Compléments aux formules de Tanaka-Rosen, Sém. de Prob. XIX, LNM1123, 332-349 Zbl0563.60073MR889493

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