The Donsker delta function of a Lévy process with application to chaos expansion of local time
Sure Mataramvura; Bernt Øksendal; Frank Proske
Annales de l'I.H.P. Probabilités et statistiques (2004)
- Volume: 40, Issue: 5, page 553-567
- ISSN: 0246-0203
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topMataramvura, Sure, Øksendal, Bernt, and 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 40.5 (2004): 553-567. <http://eudml.org/doc/77824>.
@article{Mataramvura2004,
author = {Mataramvura, Sure, Øksendal, Bernt, Proske, Frank},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Lévy processes; Local time; White noise; Donsker delta function; Chaos expansion},
language = {eng},
number = {5},
pages = {553-567},
publisher = {Elsevier},
title = {The Donsker delta function of a Lévy process with application to chaos expansion of local time},
url = {http://eudml.org/doc/77824},
volume = {40},
year = {2004},
}
TY - JOUR
AU - Mataramvura, Sure
AU - Øksendal, Bernt
AU - Proske, Frank
TI - The Donsker delta function of a Lévy process with application to chaos expansion of local time
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2004
PB - Elsevier
VL - 40
IS - 5
SP - 553
EP - 567
LA - eng
KW - Lévy processes; Local time; White noise; Donsker delta function; Chaos expansion
UR - http://eudml.org/doc/77824
ER -
References
top- [1] K. Aase, B. Øksendal, J. Ubøe, Using the Donsker delta function to compute hedging strategies, Potential Anal.14 (2001) 351-374. Zbl0993.91022MR1825691
- [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. Zbl0878.60053MR1439497
- [3] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
- [4] R.F. Bass, Local times for a class of purely discontinuous martingales, Z. Wahr. Verw. Geb.67 (1984) 433-459. Zbl0551.60047MR761566
- [5] G. Di Nunno, B. Øksendal, F. Proske, White noise analysis for Lévy processes, J. Funct. Anal.206 (2004) 109-148. Zbl1078.60054MR2024348
- [6] Y. Hu, On the self-intersection local time of Brownian motion – via chaos expansion, Publications Matemátiques40 (1996) 337-350. Zbl0878.60051
- [7] T. Hida, H.-H. Kuo, J. Potthoff, L. Streit, White Noise, Kluwer, Dordrecht, 1993. Zbl0771.60048MR1244577
- [8] Y. Hu, B. Øksendal, Chaos expansion of local time of fractional Brownian motion, Stochastic Anal. Appl.20 (2002) 815-837. Zbl1011.60016MR1921068
- [9] H. Holden, B. Øksendal, J. Ubøe, T.-S. Zhang, Stochastic Partial Differential Equations – A Modeling, White Noise Functional Approach, Birkhäuser, Boston, 1996. Zbl0860.60045
- [10] K. Itô, Spectral type of the shift transformation of differential processes and stationary increments, Trans. Amer. Math. Soc.81 (1956) 253-263. Zbl0073.35303MR77017
- [11] H.H. Kuo, White Noise Distribution Theory, in: Probab. Soch. Series, CRC Press, Boca Raton, FL, 1996. Zbl0853.60001MR1387829
- [12] Y.-J. Lee, H.-H. Shih, Donsker's delta function of Lévy processes, Acta Appl. Math.63 (2000) 219-231. Zbl0982.60067MR1834220
- [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. Zbl1053.60069
- [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. Zbl0783.60055
- [15] D. Nualart, J. Vives, Chaos expansion and local time, Publ. Math.36 (1992) 827-836. Zbl0787.60060MR1210022
- [16] N. Obata, White Noise Calculus and Fock Space, in: Lecture Notes in Math., vol. 1577, Springer-Verlag, Berlin, 1994. Zbl0814.60058MR1301775
- [17] B. Øksendal, F. Proske, White noise of Poisson random measures, Potential Anal. (2003), submitted for publication. Zbl1060.60069
- [18] K. Sato, Lévy Processes and Infinitely Divisible Distributions, in: Cambridge University Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999. Zbl0973.60001MR1739520
- [19] S. Thangavelu, Lectures on Hermite and Laguerre Expansions, in: Mathematical Notes, vol. 42, Princeton University Press, 1993. Zbl0791.41030MR1215939
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