Table of Contents
Journal of Probability
Volume 2014 (2014), Article ID 786854, 9 pages
http://dx.doi.org/10.1155/2014/786854
Research Article

Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables

Ural Federal University, No. 19, Mira Street, Ekaterinburg 620002, Russia

Received 23 November 2013; Accepted 13 February 2014; Published 7 April 2014

Academic Editor: Farrukh Mukhamedov

Copyright © 2014 M. A. Alshanskiy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. K. Itô, “Multiple Wiener integral,” Journal of the Mathematical Society of Japan, vol. 3, pp. 157–169, 1951. View at Google Scholar
  2. P. Malliavin, “Stochastic calculus of variation and hypoelliptic operators,” in Proceedings of the International Symposium on Stochastic Differential Equations. (Research Institute For Mathematical Sciences, Kyoto University, Kyoto, 1976), pp. 195–263, John Wiley & Sons, New York, NY, USA, 1978. View at Google Scholar
  3. G. da Prato, Introduction to Stochastic Analysis and Malliavin Calculus, vol. 6 of Appunti, Scuola Normale Superiore di Pisa, Edizioni della Normale, Pisa, Italy, 2007.
  4. P. Malliavin and A. Thalmaier, Stochastic Calculus of Variations in Mathematical Finance, Springer, Berlin, Germany, 2006.
  5. G. di Nunno, B. Øksendal, and F. Proske, Mallivin Calculus for Levy Processeswith Applications to Finance, Springer, Berlin, Germany, 2009.
  6. G. DaPrato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, New York, NY, USA, 1992.
  7. I. V. Melnikova and M. A. Alshanskiy, “The generalized well-posedness of the Cauchy problem for an abstract stochastic equation with multiplicative noise,” Proceedings of the Steklov Institute of Mathematics, vol. 280, supplement 1, pp. 134–150, 2013. View at Google Scholar
  8. D. A. Filipović, Consistency Problems for Heath-Jarrow-Morton Interestrate Models, vol. 1760 of Lecture notes in Mathematics, Springer, 2001.
  9. I. Ekeland and E. Taflin, “A theory of bond portfolios,” Annals of Applied Probability, vol. 15, no. 2, pp. 1260–1305, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Øksendal, Stochastic Differential Equations. An Introduction With Applications, Springer, New-York, NY, USA, 2010.