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

How to cite

top

Mataramvura, 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. [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. [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. [3] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
  4. [4] R.F. Bass, Local times for a class of purely discontinuous martingales, Z. Wahr. Verw. Geb.67 (1984) 433-459. Zbl0551.60047MR761566
  5. [5] G. Di Nunno, B. Øksendal, F. Proske, White noise analysis for Lévy processes, J. Funct. Anal.206 (2004) 109-148. Zbl1078.60054MR2024348
  6. [6] Y. Hu, On the self-intersection local time of Brownian motion – via chaos expansion, Publications Matemátiques40 (1996) 337-350. Zbl0878.60051
  7. [7] T. Hida, H.-H. Kuo, J. Potthoff, L. Streit, White Noise, Kluwer, Dordrecht, 1993. Zbl0771.60048MR1244577
  8. [8] Y. Hu, B. Øksendal, Chaos expansion of local time of fractional Brownian motion, Stochastic Anal. Appl.20 (2002) 815-837. Zbl1011.60016MR1921068
  9. [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. [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. [11] H.H. Kuo, White Noise Distribution Theory, in: Probab. Soch. Series, CRC Press, Boca Raton, FL, 1996. Zbl0853.60001MR1387829
  12. [12] Y.-J. Lee, H.-H. Shih, Donsker's delta function of Lévy processes, Acta Appl. Math.63 (2000) 219-231. Zbl0982.60067MR1834220
  13. [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. [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. [15] D. Nualart, J. Vives, Chaos expansion and local time, Publ. Math.36 (1992) 827-836. Zbl0787.60060MR1210022
  16. [16] N. Obata, White Noise Calculus and Fock Space, in: Lecture Notes in Math., vol. 1577, Springer-Verlag, Berlin, 1994. Zbl0814.60058MR1301775
  17. [17] B. Øksendal, F. Proske, White noise of Poisson random measures, Potential Anal. (2003), submitted for publication. Zbl1060.60069
  18. [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. [19] S. Thangavelu, Lectures on Hermite and Laguerre Expansions, in: Mathematical Notes, vol. 42, Princeton University Press, 1993. Zbl0791.41030MR1215939

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.