Self-intersection local time of ( α , d , β ) -superprocess

L. Mytnik; J. Villa

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 4, page 481-507
  • ISSN: 0246-0203

How to cite

top

Mytnik, L., and Villa, J.. "Self-intersection local time of $(\alpha ,d,\beta )$-superprocess." Annales de l'I.H.P. Probabilités et statistiques 43.4 (2007): 481-507. <http://eudml.org/doc/77944>.

@article{Mytnik2007,
author = {Mytnik, L., Villa, J.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {self-intersection local time; infinite variance superprocess; Tanaka-like formula},
language = {eng},
number = {4},
pages = {481-507},
publisher = {Elsevier},
title = {Self-intersection local time of $(\alpha ,d,\beta )$-superprocess},
url = {http://eudml.org/doc/77944},
volume = {43},
year = {2007},
}

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
PB - Elsevier
VL - 43
IS - 4
SP - 481
EP - 507
LA - eng
KW - self-intersection local time; infinite variance superprocess; Tanaka-like formula
UR - http://eudml.org/doc/77944
ER -

References

top
  1. [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. Zbl0786.60103MR1278075
  2. [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. Zbl0768.60066MR1166405
  3. [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. Zbl0754.60086MR1162718
  4. [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. Zbl0799.60080MR1242575
  5. [5] D. Dawson, Infinitely divisible random measure and superprocesses, in: Stochastic Analysis and Related Topics, Birkhäuser, Boston, 1992, pp. 1-130. Zbl0785.60034MR1203373
  6. [6] E. Dynkin, Representation for functionals of superprocesses by multiples stochastic integrals, with applications to self-intersection local times, Astérisque157–158 (1988) 147-171. Zbl0659.60105
  7. [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. Zbl0743.60081
  8. [8] K. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland Publishing Company and Kodansha Ltd., 1981. Zbl0495.60005MR637061
  9. [9] I. Iscoe, A weighted occupation time for a class of measure-valued branching processes, Probab. Theory Related Fields71 (1986) 85-116. Zbl0555.60034MR814663
  10. [10] J.F. Le Gall, Spatial Branching Processes Random Snakes and Partial Differential Equations, Birkhäuser, 1999. Zbl0938.60003MR1714707
  11. [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. Zbl1097.60033MR2118864
  12. [12] L. Mytnik, Collision measure and collision local time for ( α , d , β ) -superprocesses, J. Theoret. Probab.11 (3) (1998) 733-763. Zbl0917.60083MR1633395
  13. [13] L. Mytnik, E. Perkins, Regularity and irregularity of ( 1 + β ) -stable super-Brownian motion, Ann. Probab.31 (3) (2003) 1413-1440. Zbl1042.60030MR1989438
  14. [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. Zbl1108.60057MR2271487
  15. [15] J. Rosen, Renormalizations and limit theorems for self-intersections of superprocesses, Ann. Probab.20 (3) (1992) 1341-1368. Zbl0760.60024MR1175265

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.