Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times
Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 2, p. 143-176
@article{AIHPB_1999__35_2_143_0,
     author = {Rosen, Jay},
     title = {Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {2},
     year = {1999},
     pages = {143-176},
     zbl = {0922.60072},
     mrnumber = {1678521},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1999__35_2_143_0}
}
Rosen, Jay. Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times. Annales de l'I.H.P. Probabilités et statistiques, Volume 35 (1999) no. 2, pp. 143-176. http://www.numdam.org/item/AIHPB_1999__35_2_143_0/

[1] R. Bass and D. Khoshnevisan, Intersection local times and Tanaka formulas, Ann. Inst. H. Poincaré Prob. Stat., Vol. 29, 1993, pp. 419-452. | Numdam | MR 1246641 | Zbl 0798.60072

[2] J. Bertoin, Applications des processes de Dirichlet aux temps locaux et temps locaux d'intersection d'un mouvement Brownien, Prob. Theory Related Fields, Vol. 80, 1989, pp. 433-460. | MR 976535 | Zbl 0638.60083

[3] C. Goldie and J. Teugals, Regular Variation, Cambridge University Press, Cambridge, 1987. | MR 898871 | Zbl 0617.26001

[4] E.B. Dynkin, Self-intersection gauge for random walks and for Brownian motion, Ann. Probab., Vol. 16, 1988, pp. 1-57. | MR 920254 | Zbl 0638.60081

[5] B. Fristedt, Sample functions of stochastic processes with stationary independent increments, Advances in probability and related topics, Vol. 3, 1974,P. Ney and S. Port, editors, Marcel Dekker, Inc. | MR 400406 | Zbl 0309.60047

[6] J.-F. Le Gall, Proprietes d'intersection des marches aleatoires, I, Comm. Math. Phys., Vol. 104, 1986, pp. 471-507. | MR 840748 | Zbl 0609.60078

[7] J.-F. Le Gall, Fluctuation results for the Wiener sausage, Ann. Probab., Vol. 16, 1988, pp. 991-1018. | MR 942751 | Zbl 0665.60080

[8] J.-F. Le Gall, Some properties of planar Brownian motion, Ecole d'ete de probabbilities de St. Flour XX, 1990 (Berlin), Lecture Notes in Mathematics, vol. 1527, Springer-Verlag, Berlin, 1992. | MR 1229519 | Zbl 0779.60068

[9] J.-F. Le Gall and J. Rosen, The range of stable random walks, Ann. Probab., Vol. 19, 1991, pp. 650-705. | MR 1106281 | Zbl 0729.60066

[10] M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, New York, 1991. | MR 1102015 | Zbl 0748.60004

[11] M. Marcus and J. Rosen, Multiple Wick product chaos processes, preprint. | MR 1684755

[12] M. Marcus and J. Rosen, Renormalized self-intersection local times and Wick power chaos processes, Memoirs of the A.M.S., to appear. | MR 1621400

[13] J. Rosen, The asymptotics of stable sausages in the plane, Ann. Probab., Vol. 20, 1992, pp. 29-60. | MR 1143411 | Zbl 0748.60064

[14] J. Rosen, Joint continuity of renormalized intersection local times, Ann. Inst. H. Poincaré Prob. Stat., Vol. 32, 1996, pp. 671-700. | Numdam | MR 1422306 | Zbl 0867.60049

[15] S.R.S. Varadhan, Appendix to Euclidian quantum field theory by K. Symanzyk, Local Quantum Theory (R. Jost, ed.), Academic Press, 1969.