Self-intersection local time of (α,d,β)-superprocess
Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, p. 481-507
@article{AIHPB_2007__43_4_481_0,
     author = {Mytnik, L. and Villa, J.},
     title = {Self-intersection local time of $(\alpha ,d,\beta )$-superprocess},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {43},
     number = {4},
     year = {2007},
     pages = {481-507},
     doi = {10.1016/j.anihpb.2006.07.005},
     zbl = {1118.60041},
     mrnumber = {2329513},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2007__43_4_481_0}
}
Mytnik, L.; Villa, J. Self-intersection local time of $(\alpha ,d,\beta )$-superprocess. Annales de l'I.H.P. Probabilités et statistiques, Volume 43 (2007) no. 4, pp. 481-507. doi : 10.1016/j.anihpb.2006.07.005. http://www.numdam.org/item/AIHPB_2007__43_4_481_0/

[1] R.J. Adler, Superprocess local and intersection local times and their corresponding particle pictures, in: Seminar on Stochastic Processes, 1992, Birkhäuser, 1993, pp. 1-42. | MR 1278075 | Zbl 0786.60103

[2] R.J. Adler, M. Lewin, An evolution equation for the intersection local times of superprocesses, in: Barlow M.T., Bingham N.H. (Eds.), Stochastic Analysis, 1991, pp. 1-22. | MR 1166405 | Zbl 0768.60066

[3] R.J. Adler, M. Lewin, Local time and Tanaka formulae for super Brownian motion and super stable processes, Stochastic Process. Appl. 41 (1992) 45-67. | MR 1162718 | Zbl 0754.60086

[4] D. Dawson, Measure-valued Markov processes, in: École d'Été de Probabilitiés de Saint Flour XXI, Lecture Notes in Math., vol. 1541, Springer, Berlin, 1993, pp. 1-260. | MR 1242575 | Zbl 0799.60080

[5] D. Dawson, Infinitely divisible random measure and superprocesses, in: Stochastic Analysis and Related Topics, Birkhäuser, Boston, 1992, pp. 1-130. | MR 1203373 | Zbl 0785.60034

[6] E. Dynkin, Representation for functionals of superprocesses by multiples stochastic integrals, with applications to self-intersection local times, Astérisque 157-158 (1988) 147-171. | Zbl 0659.60105

[7] N. El Karoui, S. Roelly, Propriétés de martingales, explosion et représentation de Lévy-Khintchine d'une classe de processus de branchement à valeurs measures, Stochastic Process. Appl. 38 (1991) 239-266. | Zbl 0743.60081

[8] K. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland Publishing Company and Kodansha Ltd., 1981. | MR 637061 | Zbl 0495.60005

[9] I. Iscoe, A weighted occupation time for a class of measure-valued branching processes, Probab. Theory Related Fields 71 (1986) 85-116. | MR 814663 | Zbl 0555.60034

[10] J.F. Le Gall, Spatial Branching Processes Random Snakes and Partial Differential Equations, Birkhäuser, 1999. | MR 1714707 | Zbl 0938.60003

[11] J.F. Le Gall, L. Mytnik, Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion, Ann. Probab. 33 (1) (2005) 194-222. | MR 2118864 | Zbl 1097.60033

[12] L. Mytnik, Collision measure and collision local time for (α,d,β)-superprocesses, J. Theoret. Probab. 11 (3) (1998) 733-763. | MR 1633395 | Zbl 0917.60083

[13] L. Mytnik, E. Perkins, Regularity and irregularity of (1+β)-stable super-Brownian motion, Ann. Probab. 31 (3) (2003) 1413-1440. | MR 1989438 | Zbl 1042.60030

[14] L. Mytnik, E. Perkins, A. Sturm, On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients, Ann. Probab. 34 (5) (2006) 1910-1959. | MR 2271487 | Zbl 1108.60057

[15] J. Rosen, Renormalizations and limit theorems for self-intersections of superprocesses, Ann. Probab. 20 (3) (1992) 1341-1368. | MR 1175265 | Zbl 0760.60024