Besov regularity for the generalized local time of the indefinite Skorohod integral

 Access to full text

 Full (PDF)

1. [1] M.T. Barlow, M. Yor, Semimartingale inequalities via the Garsia–Rodemich–Rumsey lemma, and applications to local times, J. Funct. Anal.49 (1982) 198-229. Zbl0505.60054
2. [2] J. Bergh, J. Löfström, Interpolation Spaces – An Introduction, Springer-Verlag, World Publishing Corp., 1976, 2003. Zbl0344.46071
3. [3] A. Berkaoui, Y. Ouknine, Régularité Besov des trajectoires du processus intégral de Skorohod, Bull. Sci. Math.123 (1999) 643-663. MR1725208
4. [4] B. Boufoussi, B. Roynette, Le temps local brownien appartient p.s. l’espace de Besov $B_{p,\alpha }^{1/2}$, C. R. Acad. Sci. Paris Ser. I Math.316 (1993) 843-848. Zbl0788.46035MR1218273
5. [5] Z. Ciesielski, G. Kerkyacharian, B. Roynette, Quelques espaces fonctionnels associés des processus gaussiens, Studia Math.107 (1993) 171-204. Zbl0809.60004MR1244574
6. [6] D. Geman, J. Horowitz, Occupation densities, Ann. Probab.8 (1980) 1-67. Zbl0499.60081MR556414
7. [7] P. Imkeller, Occupation densities for stochastic integral processes in the second Wiener chaos, Probab. Theory Related Fields91 (1992) 1-24. Zbl0744.60055MR1142759
8. [8] P. Imkeller, D. Nualart, Integration by parts on Wiener space and the existence of occupation densities, Ann. Probab.22 (1994) 469-493. Zbl0803.60049MR1258887
9. [9] H. Lakhel, Y. Ouknine, C.A. Tudor, Besov regularity for the indefinite Skorohod integral with respect to the fractional Brownian motion: the singular case, Stochastics Stochastics Rep.74 (2002) 597-615. Zbl1010.60048MR1943581
10. [10] Z. Liang, Besov-regularity of local times of some semimartingales, Preprint, 2005. 
11. [11] P. Malliavin, Stochastic Analysis, Grundlehren Math. Wiss., vol. 313, Springer-Verlag, Berlin, 1997, (xii+343 pp.). Zbl0878.60001MR1450093
12. [12] D. Nualart, The Malliavin Calculus and Related Topics, Probab. Appl., Springer-Verlag, New York, 1995, (xii+266 pp.). Zbl0837.60050MR1344217
13. [13] D. Nualart, Y. Ouknine, Besov regularity of stochastic integrals with respect to the fractional Brownian motion with parameter $Hgt;\frac{1}{2}$, J. Theoret. Probab.16 (2003) 451-470. Zbl1027.60052MR1982038
14. [14] C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli10 (2004) 313-325. Zbl1062.60055MR2046776
15. [15] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. Zbl0387.46032MR503903
16. [16] Y. Xiao, T. Zhang, Local times of fractional Brownian sheets, Probab. Theory Related Fields124 (2002) 204-226. Zbl1009.60024MR1936017