Self-intersection local time of (α,d,β)-superprocess
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 4, pp. 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},
     pages = {481--507},
     publisher = {Elsevier},
     volume = {43},
     number = {4},
     year = {2007},
     doi = {10.1016/j.anihpb.2006.07.005},
     mrnumber = {2329513},
     zbl = {1118.60041},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2006.07.005/}
}
TY  - JOUR
AU  - Mytnik, L.
AU  - Villa, J.
TI  - Self-intersection local time of $(\alpha ,d,\beta )$-superprocess
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2007
SP  - 481
EP  - 507
VL  - 43
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2006.07.005/
DO  - 10.1016/j.anihpb.2006.07.005
LA  - en
ID  - AIHPB_2007__43_4_481_0
ER  - 
%0 Journal Article
%A Mytnik, L.
%A Villa, J.
%T Self-intersection local time of $(\alpha ,d,\beta )$-superprocess
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2007
%P 481-507
%V 43
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2006.07.005/
%R 10.1016/j.anihpb.2006.07.005
%G en
%F 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, Tome 43 (2007) no. 4, pp. 481-507. doi : 10.1016/j.anihpb.2006.07.005. http://www.numdam.org/articles/10.1016/j.anihpb.2006.07.005/

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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. | Numdam | Zbl

[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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

Cité par Sources :