Joint continuity and a Doob-Meyer type decomposition for renormalized intersection local times

 Access to full text

 Full (PDF)

1. [1] R. Bass and D. Khoshnevisan, Intersection local times and Tanaka formulas, Ann. Inst. H. Poincaré Prob. Stat., Vol. 29, 1993, pp. 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, Prob. Theory Related Fields, Vol. 80, 1989, pp. 433-460. Zbl0638.60083MR976535
3. [3] C. Goldie and J. Teugals, Regular Variation, Cambridge University Press, Cambridge, 1987. Zbl0617.26001MR898871
4. [4] E.B. Dynkin, Self-intersection gauge for random walks and for Brownian motion, Ann. Probab., Vol. 16, 1988, pp. 1-57. Zbl0638.60081MR920254
5. [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. Zbl0309.60047MR400406
6. [6] J.-F. Le Gall, Proprietes d'intersection des marches aleatoires, I, Comm. Math. Phys., Vol. 104, 1986, pp. 471-507. Zbl0609.60078MR840748
7. [7] J.-F. Le Gall, Fluctuation results for the Wiener sausage, Ann. Probab., Vol. 16, 1988, pp. 991-1018. Zbl0665.60080MR942751
8. [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. Zbl0779.60068MR1229519
9. [9] J.-F. Le Gall and J. Rosen, The range of stable random walks, Ann. Probab., Vol. 19, 1991, pp. 650-705. Zbl0729.60066MR1106281
10. [10] M. Ledoux and M. Talagrand, Probability in Banach spaces, Springer-Verlag, New York, 1991. Zbl0748.60004MR1102015
11. [11] M. Marcus and J. Rosen, Multiple Wick product chaos processes, preprint. Zbl1105.60304MR1684755
12. [12] M. Marcus and J. Rosen, Renormalized self-intersection local times and Wick power chaos processes, Memoirs of theA.M.S., to appear. Zbl1230.60005MR1621400
13. [13] J. Rosen, The asymptotics of stable sausages in the plane, Ann. Probab., Vol. 20, 1992, pp. 29-60. Zbl0748.60064MR1143411
14. [14] J. Rosen, Joint continuity of renormalized intersection local times, Ann. Inst. H. Poincaré Prob. Stat., Vol. 32, 1996, pp. 671-700. Zbl0867.60049MR1422306
15. [15] S.R.S. Varadhan, Appendix to Euclidian quantum field theory by K. Symanzyk, Local Quantum Theory (R. Jost, ed.), Academic Press, 1969. 

1. Jay Rosen, Dirichlet processes and an intrinsic characterization of renormalized intersection local times
2. Jay S. Rosen, Continuous differentiability of renormalized intersection local times in R1