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References
[A1] R.J. Adler (1981). The Geometry of Random Fields, Wiley, London
[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
[BBK] R.F. Bass, K. Burdzy and D. Khoshnevisan (1994). Intersection local time for points of infinite multiplicity, Ann. Prob., 22, 566–625
[BK] R.F. Bass and D. Khoshnevisan (1993). Intersection local times and Tanaka formulas, Ann. Inst. Henri Poincaré: Prob. et Stat., 29, 419–451
[BG] R. Blumenthal and R.K. Getoor (1968). Markov Processes and Potential Theory. Academic Press, New York
[C] X. Chen (1994). Hausdorff dimension of multiple points of the (N,d) Wiener process, Indiana Univ. Math. J., 43(1), 55–60
[DEK1] A. Dvoretsky, P. Erdős and S. Kakutani (1950). Double points of paths of Brownian motion in n-space, Acta. Sci. Math. (Szeged), 12, 74–81
[DEK2] A. Dvoretsky, P. Erdős and S. Kakutani (1954). Multiple points of Brownian motion in the plane, Bull. Res. Council Israel Section F, 3, 364–371
[DEKT] A. Dvoretsky, P. Erdős, S. Kakutani and S.J. Taylor (1957). Triple points of Brownian motion in 3-space, Proc. Camb. Phil. Soc., 53, 856–862
[D1] E.B. Dynkin (1988). Self-intersection gauge for random walks and for Brownian motion, Ann. Prob., 16, 1–57
[D2] E.B. Dynkin (1985). Random fields associated with multiple points of Brownian motion, J. Funct. Anal., 62 397–434
[E] W. Ehm (1981). Sample function properties of multiparameter stable processes, Zeit. Wahr. verw. Geb., 56, 195–228
[E1] S.N. Evans (1987) Multiple points in the sample paths of a Lévy process, Prob. Th. Rel. Fields, 76, 359–367
[E2] S.N. Evans (1987) Potential theory for a family of several Markov processes, Ann. Inst. Henri Poincaré: Prob. et Stat., 23, 499–530
[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
[FS-2] P.J. Fitzsimmons and T.S. Salisbury Forthcoming Manuscript.
[F] B. Fristedt (1995). Math. Reviews, review 95b:60100, February 1995 issue
[HaP] J. Hawkes and W.E. Pruitt (1974). Uniform dimension results for processes with independent increments, Zeit. Wahr. verw. Geb., 28, 277–288
[H] W.J. Hendricks (1974). Multiple points for transient symmetric Lévy processes, Zeit. Wahr. verw. Geb. 49, 13–21
[K] J.P. Kahane (1985). Some Random Series of Functions, Cambridge Univ. Press, Cambridge, U.K.
[Ka] R. Kaufman (1969). Une propriété métrique du mouvement brownien, C.R. Acad. Sci. Paris, Sér. A, 268, 727–728
[LG] J.F. LeGall (1990). Some Properties of Planar Brownian Motion, Ecole d’été de Probabilités de St-Flour XX, LNM 1527, 111–235
[OP] S. Orey and W.E. Pruitt (1973). Sample functions of the N-parameter Wiener process, Ann. Prob., 1, 138–163
[P] Y. Peres (1995). Intersection-equivalence of Brownian paths and certain branching processes. Comm. Math. Phys. (To appear)
[R1] J. Rosen (1995). Joint continuity of renormalized intersection local times. Preprint
[R2] J. Rosen (1984). Stochastic integrals and intersections of Brownian sheet. Unpublished manuscript
[R3] J. Rosen (1984). Self-intersections of random fields, Ann. Prob., 12, 108–119
[S] T.S. Salisbury (1995). Energy, and intersections of Markov chains, Proceedings of the IMA Workshop on Random Discrete Structures (To appear)
[Sh] N.-R. Shieh (1991). White noise analysis and Tanaka formulæ for intersections of planar Brownian motion, Nagoya Math. J., 122, 1–17
[T1] S.J. Taylor (1986). The measure theory of random fractals. Math. Proc. Camb. Phil Soc., 100, 383–406
[T2] S.J. Taylor (19. Multiple points for the sample paths of a transient stable process, J. Math. Mech. 16, 1229–1246
[T3] S.J. Taylor (1966). Multiple points for the sample paths of the symmetric stable process, Zeit. Wahr. verw. Geb., 5, 247–264
[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
[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
[Y] M. Yor (1985). Compléments aux formules de Tanaka-Rosen, Sém. de Prob. XIX, LNM 1123, 332–349
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Khoshnevisan, D. (1997). Some polar sets for the Brownian sheet. In: Azéma, J., Yor, M., Emery, M. (eds) Séminaire de Probabilités XXXI. Lecture Notes in Mathematics, vol 1655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0119303
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