The Donsker delta function of a Lévy process with application to chaos expansion of local time
Mataramvura, Sure ; Øksendal, Bernt ; Proske, Frank
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004), p. 553-567 / Harvested from Numdam
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@article{AIHPB_2004__40_5_553_0,
     author = {Mataramvura, Sure and \O ksendal, Bernt and Proske, Frank},
     title = {The Donsker delta function of a L\'evy process with application to chaos expansion of local time},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {40},
     year = {2004},
     pages = {553-567},
     doi = {10.1016/j.anihpb.2004.01.002},
     mrnumber = {2086014},
     zbl = {1053.60047},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_5_553_0}
}

Mataramvura, Sure; Øksendal, Bernt; Proske, Frank. The Donsker delta function of a Lévy process with application to chaos expansion of local time. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 553-567. doi : 10.1016/j.anihpb.2004.01.002. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_5_553_0/

[1] K. Aase, B. Øksendal, J. Ubøe, Using the Donsker delta function to compute hedging strategies, Potential Anal. 14 (2001) 351-374. | MR 1825691 | Zbl 0993.91022

[2] S. Albeverio, Y. Hu, X.Y. Zhou, A remark on nonsmoothness of self intersection local time of planar Brownian motion, Statist. Probab. Lett. 32 (1997) 57-65. | MR 1439497 | Zbl 0878.60053

[3] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. | MR 1406564 | Zbl 0861.60003

[4] R.F. Bass, Local times for a class of purely discontinuous martingales, Z. Wahr. Verw. Geb. 67 (1984) 433-459. | MR 761566 | Zbl 0551.60047

[5] G. Di Nunno, B. Øksendal, F. Proske, White noise analysis for Lévy processes, J. Funct. Anal. 206 (2004) 109-148. | MR 2024348 | Zbl 1078.60054

[6] Y. Hu, On the self-intersection local time of Brownian motion - via chaos expansion, Publications Matemátiques 40 (1996) 337-350. | Zbl 0878.60051

[7] T. Hida, H.-H. Kuo, J. Potthoff, L. Streit, White Noise, Kluwer, Dordrecht, 1993. | MR 1244577 | Zbl 0771.60048

[8] Y. Hu, B. Øksendal, Chaos expansion of local time of fractional Brownian motion, Stochastic Anal. Appl. 20 (2002) 815-837. | MR 1921068 | Zbl 1011.60016

[9] H. Holden, B. Øksendal, J. Ubøe, T.-S. Zhang, Stochastic Partial Differential Equations - A Modeling, White Noise Functional Approach, Birkhäuser, Boston, 1996. | Zbl 0860.60045

[10] K. Itô, Spectral type of the shift transformation of differential processes and stationary increments, Trans. Amer. Math. Soc. 81 (1956) 253-263. | MR 77017 | Zbl 0073.35303

[11] H.H. Kuo, White Noise Distribution Theory, in: Probab. Soch. Series, CRC Press, Boca Raton, FL, 1996. | MR 1387829 | Zbl 0853.60001

[12] Y.-J. Lee, H.-H. Shih, Donsker's delta function of Lévy processes, Acta Appl. Math. 63 (2000) 219-231. | MR 1834220 | Zbl 0982.60067

[13] A. Løkka, B. Øksendal, F. Proske, Stochastic partial differential equations driven by Lévy space-time white noise, Ann. Appl. Probab. (2003), submitted for publication. | Zbl 1053.60069

[14] T. Lindstrøm, B. Øksendal, J. Ubøe, Stochastic differential equations involving positive noise, in: Barlow M., Bingham N. (Eds.), Stochastic Analysis, Cambridge Univ. Press, Cambridge, 1991, pp. 261-303. | Zbl 0783.60055

[15] D. Nualart, J. Vives, Chaos expansion and local time, Publ. Math. 36 (1992) 827-836. | MR 1210022 | Zbl 0787.60060

[16] N. Obata, White Noise Calculus and Fock Space, in: Lecture Notes in Math., vol. 1577, Springer-Verlag, Berlin, 1994. | MR 1301775 | Zbl 0814.60058

[17] B. Øksendal, F. Proske, White noise of Poisson random measures, Potential Anal. (2003), submitted for publication. | Zbl 1060.60069

[18] K. Sato, Lévy Processes and Infinitely Divisible Distributions, in: Cambridge University Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999. | MR 1739520 | Zbl 0973.60001

[19] S. Thangavelu, Lectures on Hermite and Laguerre Expansions, in: Mathematical Notes, vol. 42, Princeton University Press, 1993. | MR 1215939 | Zbl 0791.41030