Dirichlet processes and an intrinsic characterization of renormalized intersection local times

Jay Rosen

Annales de l'I.H.P. Probabilités et statistiques (2001)

  • Volume: 37, Issue: 4, page 403-420
  • ISSN: 0246-0203

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Rosen, Jay. "Dirichlet processes and an intrinsic characterization of renormalized intersection local times." Annales de l'I.H.P. Probabilités et statistiques 37.4 (2001): 403-420. <http://eudml.org/doc/77694>.

@article{Rosen2001,
author = {Rosen, Jay},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {intersection local time; continuous additive functional; Lévy process; stable process; Dirichlet process; Doob-Meyer decomposition; quadratic variation},
language = {eng},
number = {4},
pages = {403-420},
publisher = {Elsevier},
title = {Dirichlet processes and an intrinsic characterization of renormalized intersection local times},
url = {http://eudml.org/doc/77694},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Rosen, Jay
TI - Dirichlet processes and an intrinsic characterization of renormalized intersection local times
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2001
PB - Elsevier
VL - 37
IS - 4
SP - 403
EP - 420
LA - eng
KW - intersection local time; continuous additive functional; Lévy process; stable process; Dirichlet process; Doob-Meyer decomposition; quadratic variation
UR - http://eudml.org/doc/77694
ER -

References

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  1. [1] R Bass, D Khoshnevisan, Intersection local times and Tanaka formulas, Ann. Inst. H. Poincaré Probab. Stat.29 (1993) 419-452. Zbl0798.60072MR1246641
  2. [2] J Bertoin, Applications des processes de Dirichlet aux temps locaux et temps locaux d'intersection d'un mouvement Brownien, Probab. Theory Related Fields80 (1989) 433-460. Zbl0638.60083MR976535
  3. [3] R Blumenthal, R Getoor, Some theorems on stable proceses, Trans. Amer. Math. Soc.95 (1960) 261-273. Zbl0107.12401MR119247
  4. [4] E.B Dynkin, Self-intersection gauge for random walks and for Brownian motion, Ann. Probab.16 (1988) 1-57. Zbl0638.60081MR920254
  5. [5] P Fitzsimmons, T Salisbury, Capacity and energy for multiparameter Markov processes, Ann. Inst. H. Poincaré Probab. Stat.25 (1989) 325-350. Zbl0689.60071MR1023955
  6. [6] H Föllmer, Dirichlet processes, in: Proceedings Durham 1980 (Berlin), Lecture Notes Math., 851, Springer-Verlag, Berlin, 1981, pp. 476-478. Zbl0462.60046MR621001
  7. [7] J.-F Le Gall, Proprietes d'intersection des marches aleatoires, I, Comm. Math. Phys.104 (1986) 471-507. Zbl0609.60078MR840748
  8. [8] J.-F Le Gall, Fluctuation results for the Wiener sausage, Ann. Probab.16 (1988) 991-1018. Zbl0665.60080MR942751
  9. [9] 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, 1527, Springer-Verlag, Berlin, 1992. Zbl0779.60068MR1229519
  10. [10] J.-F Le Gall, J Rosen, The range of stable random walks, Ann. Probab.19 (1991) 650-705. Zbl0729.60066MR1106281
  11. [11] M Marcus, J Rosen, Renormalized self-intersection local times and Wick power chaos processes, Mem. Amer. Math. Soc.142 (675) (1999). Zbl1230.60005MR1621400
  12. [12] J Rosen, Joint continuity and a Doob–Meyer type decomposition for renormalized intersection local times, Ann. Inst. H. Poincaré Probab. Stat.35 (1999) 143-176. Zbl0922.60072MR1678521
  13. [13] J Rosen, Continuity and singularity of the intersection local time of stable processes in R2, Ann. Probab.16 (1988) 75-79. Zbl0644.60078MR920256
  14. [14] J Rosen, The asymptotics of stable sausages in the plane, Ann. Probab.20 (1992) 29-60. Zbl0748.60064MR1143411
  15. [15] J Rosen, Joint continuity of renormalized intersection local times, Ann. Inst. H. Poincaré Probab. Stat.32 (1996) 671-700. Zbl0867.60049MR1422306
  16. [16] S.R.S Varadhan, Appendix to Euclidian quantum field theory by K. Symanzyk, in: Jost R (Ed.), Local Quantum Theory, Academic Press, 1969. 

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